Systems and methods for improved sustainment of a high performance frc elevated energies utilizing neutral beam injectors with tunable beam energies

ABSTRACT

Systems and methods that facilitate forming and maintaining FRCs with superior stability as well as particle, energy and flux confinement and, more particularly, systems and methods that facilitate forming and maintaining FRCs with elevated system energies and improved sustainment utilizing neutral beam injectors with tunable beam energy capabilities.

CROSS-REFERENCE TO RELATED APPLICATIONS

The subject application is a continuation of PCT Patent Application No.PCT/US17/59067, filed Oct. 30, 2017, which claims priority to U.S.Provisional Patent Application No. 62/414,574, filed on Oct. 28, 2016,both of which are incorporated by reference herein in their entiretiesfor all purposes.

FIELD

The subject matter described herein relates generally to magnetic plasmaconfinement systems having a field reversed configuration (FRC) and,more particularly, to systems and methods that facilitate forming andmaintaining FRCs with superior stability as well as particle, energy andflux confinement and, more particularly, to systems and methods thatfacilitate forming and maintaining FRCs with elevated system energiesand improved sustainment utilizing neutral beam injectors with tunablebeam energy capabilities.

BACKGROUND INFORMATION

The Field Reversed Configuration (FRC) belongs to the class of magneticplasma confinement topologies known as compact toroids (CT). It exhibitspredominantly poloidal magnetic fields and possesses zero or smallself-generated toroidal fields (see M. Tuszewski, Nucl. Fusion 28, 2033(1988)). The attractions of such a configuration are its simple geometryfor ease of construction and maintenance, a natural unrestricteddivertor for facilitating energy extraction and ash removal, and veryhigh β (β is the ratio of the average plasma pressure to the averagemagnetic field pressure inside the FRC), i.e., high power density. Thehigh β nature is advantageous for economic operation and for the use ofadvanced, aneutronic fuels such as D-He³ and p-B¹¹.

The traditional method of forming an FRC uses the field-reversed θ-pinchtechnology, producing hot, high-density plasmas (see A. L. Hoffman andJ. T. Slough, Nucl. Fusion 33, 27 (1993)). A variation on this is thetranslation-trapping method in which the plasma created in a theta-pinch“source” is more-or-less immediately ejected out one end into aconfinement chamber. The translating plasmoid is then trapped betweentwo strong mirrors at the ends of the chamber (see, for instance, H.Himura, S. Okada, S. Sugimoto, and S. Goto, Phys. Plasmas 2, 191(1995)). Once in the confinement chamber, various heating and currentdrive methods may be applied such as beam injection (neutral orneutralized), rotating magnetic fields, RF or ohmic heating, etc. Thisseparation of source and confinement functions offers key engineeringadvantages for potential future fusion reactors. FRCs have proved to beextremely robust, resilient to dynamic formation, translation, andviolent capture events. Moreover, they show a tendency to assume apreferred plasma state (see e.g. H. Y. Guo, A. L. Hoffman, K. E. Miller,and L. C. Steinhauer, Phys. Rev. Lett. 92, 245001 (2004)). Significantprogress has been made in the last decade developing other FRC formationmethods: merging spheromaks with oppositely-directed helicities (seee.g. Y. Ono, M. Inomoto, Y. Ueda, T. Matsuyama, and T. Okazaki, Nucl.Fusion 39, 2001 (1999)) and by driving current with rotating magneticfields (RMF) (see e.g. I. R. Jones, Phys. Plasmas 6, 1950 (1999)) whichalso provides additional stability.

Recently, the collision-merging technique, proposed long ago (see e.g.D. R. Wells, Phys. Fluids 9, 1010 (1966)) has been significantlydeveloped further: two separate theta-pinches at opposite ends of aconfinement chamber simultaneously generate two plasmoids and acceleratethe plasmoids toward each other at high speed; they then collide at thecenter of the confinement chamber and merge to form a compound FRC. Inthe construction and successful operation of one of the largest FRCexperiments to date, the conventional collision-merging method was shownto produce stable, long-lived, high-flux, high temperature FRCs (seee.g. M. Binderbauer, H. Y. Guo, M. Tuszewski et al., Phys. Rev. Lett.105, 045003 (2010)).

FRCs consist of a torus of closed field lines inside a separatrix, andof an annular edge layer on the open field lines just outside theseparatrix. The edge layer coalesces into jets beyond the FRC length,providing a natural divertor. The FRC topology coincides with that of aField-Reversed-Mirror plasma. However, a significant difference is thatthe FRC plasma has a β of about 10. The inherent low internal magneticfield provides for a certain indigenous kinetic particle population,i.e. particles with large larmor radii, comparable to the FRC minorradius. It is these strong kinetic effects that appear to at leastpartially contribute to the gross stability of past and present FRCs,such as those produced in the collision-merging experiment.

Typical past FRC experiments have been dominated by convective losseswith energy confinement largely determined by particle transport.Particles diffuse primarily radially out of the separatrix volume, andare then lost axially in the edge layer. Accordingly, FRC confinementdepends on the properties of both closed and open field line regions.The particle diffusion time out of the separatrix scales asτ_(⊥)˜a²/D_(⊥) (a˜r_(s)/4, where r_(s) is the central separatrixradius), and D_(⊥) is a characteristic FRC diffusivity, such asD_(⊥)˜12.5 ρ_(ie), with ρ_(ie) representing the ion gyroradius,evaluated at an externally applied magnetic field. The edge layerparticle confinement time τ_(∥) is essentially an axial transit time inpast FRC experiments. In steady-state, the balance between radial andaxial particle losses yields a separatrix density gradient lengthδ˜(D_(⊥)τ_(∥))^(1/2). The FRC particle confinement time scales as(τ_(⊥)τ_(∥))^(1/2) for past FRCs that have substantial density at theseparatrix (see e.g. M. TUSZEWSKI, “Field Reversed Configurations,”Nucl. Fusion 28, 2033 (1988)).

Another drawback of prior FRC system designs was the need to useexternal multipoles to control rotational instabilities such as the fastgrowing n=2 interchange instabilities. In this way the typicalexternally applied quadrupole fields provided the required magneticrestoring pressure to dampen the growth of these unstable modes. Whilethis technique is adequate for stability control of the thermal bulkplasma, it poses a severe problem for more kinetic FRCs or advancedhybrid FRCs, where a highly kinetic large orbit particle population iscombined with the usual thermal plasma. In these systems, thedistortions of the axisymmetric magnetic field due to such multipolefields leads to dramatic fast particle losses via collision-lessstochastic diffusion, a consequence of the loss of conservation ofcanonical angular momentum. A novel solution to provide stabilitycontrol without enhancing diffusion of any particles is, thus, importantto take advantage of the higher performance potential of thesenever-before explored advanced FRC concepts.

In light of the foregoing, it is, therefore, desirable to improve thesustainment of FRCs in order to use steady state FRCs with elevatedenergy systems as a pathway to a reactor core for fusion of light nucleifor the future generation of energy.

SUMMARY

The present embodiments provided herein are directed to systems andmethods that facilitate forming and maintaining FRCs with superiorstability as well as particle, energy and flux confinement and, moreparticularly, to systems and methods that facilitate forming andmaintaining FRCs with elevated system energies and improved sustainmentutilizing neutral beam injectors with tunable beam energy capabilities.According to an embodiment of the present disclosure, a method forgenerating and maintaining a magnetic field with a field reversedconfiguration (FRC) comprises forming an FRC about a plasma in aconfinement chamber, and injecting a plurality of neutral beams into theFRC plasma while tuning the beam energies of the plurality of neutralbeams between a first beam energy and a second beam energy, wherein thesecond beam energy differs from the first beam energy.

According to a further embodiment of the present disclosure, theplurality of neutral beams switch between the first and second beamenergies during the duration of an injection shot.

According to a further embodiment of the present disclosure, the methodincludes adjusting the beam energies of the plurality of neutral beamsto adjust the radial beam power deposition profile to adjust thepressure gradient value.

According to a further embodiment of the present disclosure, the methodfurther includes maintaining the FRC at or about a constant valuewithout decay and elevating the plasma temperature to above about 1.0keV by injecting beams of fast neutral atoms from neutral beam injectorsinto the FRC plasma at an angle towards the mid through plane of theconfinement chamber.

According to a further embodiment of the present disclosure, the methodfurther comprising injecting compact toroid (CT) plasmas from first andsecond CT injectors into the FRC plasma at an angle towards themid-plane of the confinement chamber, wherein the first and second CTinjectors are diametrically opposed on opposing sides of the mid-planeof the confinement chamber.

According to an embodiment of the present disclosure, a system forgenerating and maintaining a magnetic field with a field reversedconfiguration (FRC) comprising: a confinement chamber; first and seconddiametrically opposed FRC formation sections coupled to the first andsecond diametrically opposed inner divertors; first and second divertorscoupled to the first and second formation sections; one or more of aplurality of plasma guns, one or more biasing electrodes and first andsecond mirror plugs, wherein the plurality of plasma guns includes firstand second axial plasma guns operably coupled to the first and seconddivertors, the first and second formation sections and the confinementchamber, wherein the one or more biasing electrodes being positionedwithin one or more of the confinement chamber, the first and secondformation sections, and the first and second outer divertors, andwherein the first and second mirror plugs being position between thefirst and second formation sections and the first and second divertors;a gettering system coupled to the confinement chamber and the first andsecond divertors; a plurality of neutral atom beam injectors coupled tothe confinement chamber and angled toward a mid-plane of the confinementchamber, wherein one or more of the plurality of neutral atom beaminjectors are tunable between a first beam energy and a second beamenergy, wherein the second beam energy differ from the first beamenergy; and a magnetic system comprising a plurality of quasi-dc coilspositioned around the confinement chamber, the first and secondformation sections, and the first and second divertors, and first andsecond set of quasi-dc mirror coils positioned between the first andsecond formation sections and the first and second divertors.

According to a further embodiment of the present disclosure, the systemfurther comprising first and second compact toroid (CT) injectorscoupled to the confinement chamber at an angle towards the mid-plane ofthe confinement chamber, wherein the first and second CT injectors arediametrically opposed on opposing sides of the mid-plane of theconfinement chamber.

The systems, methods, features and advantages of the example embodimentswill be or will become apparent to one with skill in the art uponexamination of the following figures and detailed description. It isintended that all such additional methods, features and advantages beincluded within this description, and be protected by the accompanyingclaims. It is also intended that the claims are not limited to requirethe details of the example embodiments.

BRIEF DESCRIPTION OF THE FIGURES

The accompanying drawings, which are included as part of the presentspecification, illustrate the presently example embodiments and,together with the general description given above and the detaileddescription of the example embodiments given below, serve to explain andteach the principles of the present invention.

FIG. 1 illustrates particle confinement in the present FRC system undera high performance FRC regime (HPF) versus under a conventional FRCregime (CR), and versus other conventional FRC experiments.

FIG. 2 illustrates the components of the present FRC system and themagnetic topology of an FRC producible in the present FRC system.

FIG. 3A illustrates the basic layout of the present FRC system as viewedfrom the top, including the preferred arrangement of the centralconfinement vessel, formation section, divertors, neutral beams,electrodes, plasma guns, mirror plugs and pellet injector.

FIG. 3B illustrates the central confinement vessel as viewed from thetop and showing the neutral beams arranged at an angle normal to themajor axis of symmetry in the central confinement vessel.

FIG. 3C illustrates the central confinement vessel as viewed from thetop and showing the neutral beams arranged at an angle less than normalto the major axis of symmetry in the central confinement vessel anddirected to inject particles toward the mid-plane of the centralconfinement vessel.

FIGS. 3D and 3E illustrate top and perspective views, respectively, ofthe basic layout of an alternative embodiment of the present FRC system,including the preferred arrangement of the central confinement vessel,formation section, inner and outer divertors, neutral beams arranged atan angle less than normal to the major axis of symmetry in the centralconfinement vessel, electrodes, plasma guns and mirror plugs.

FIG. 4 illustrates a schematic of the components of a pulsed powersystem for the formation sections.

FIG. 5 illustrates an isometric view of an individual pulsed powerformation skid.

FIG. 6 illustrates an isometric view of a formation tube assembly.

FIG. 7 illustrates a partial sectional isometric view of neutral beamsystem and key components.

FIG. 8 illustrates an isometric view of the neutral beam arrangement onconfinement chamber.

FIG. 9 illustrates a partial sectional isometric view of a preferredarrangement of the Ti and Li gettering systems.

FIG. 10 illustrates a partial sectional isometric view of a plasma guninstalled in the divertor chamber. Also shown are the associatedmagnetic mirror plug and a divertor electrode assembly.

FIG. 11 illustrates a preferred layout of an annular bias electrode atthe axial end of the confinement chamber.

FIG. 12 illustrates the evolution of the excluded flux radius in the FRCsystem obtained from a series of external diamagnetic loops at the twofield reversed theta pinch formation sections and magnetic probesembedded inside the central metal confinement chamber. Time is measuredfrom the instant of synchronized field reversal in the formationsources, and distance z is given relative to the axial midplane of themachine.

FIGS. 13A, 13B, 13C and 13D illustrate data from a representativenon-HPF, un-sustained discharge on the present FRC system. Shown asfunctions of time are (FIG. 13A) excluded flux radius at the midplane,(FIG. 13B) 6 chords of line-integrated density from the midplane CO2interferometer, (FIG. 13C) Abel-inverted density radial profiles fromthe CO2 interferometer data, and (FIG. 13D) total plasma temperaturefrom pressure balance.

FIG. 14 illustrates the excluded flux axial profiles at selected timesfor the same discharge of the present FRC system shown in FIGS. 13A,13B, 13C and 13D.

FIG. 15 illustrates an isometric view of the saddle coils mountedoutside of the confinement chamber.

FIGS. 16A, 16B, 16C and 16D illustrate the correlations of FRC lifetimeand pulse length of injected neutral beams. As shown, longer beam pulsesproduce longer lived FRCs.

FIGS. 17A, 17B, 17C and 17D the individual and combined effects ofdifferent components of the FRC system on FRC performance and theattainment of the HPF regime.

FIGS. 18A, 18B, 18C and 18D illustrate data from a representative HPF,un-sustained discharge on the present FRC system. Shown as functions oftime are (FIG. 18A) excluded flux radius at the midplane, (FIG. 18B) 6chords of line-integrated density from the midplane CO2 interferometer,(FIG. 18C) Abel-inverted density radial profiles from the CO2interferometer data, and (FIG. 18D) total plasma temperature frompressure balance.

FIG. 19 illustrates flux confinement as a function of electrontemperature (T_(e)). It represents a graphical representation of a newlyestablished superior scaling regime for HPF discharges.

FIG. 20 illustrates the FRC lifetime corresponding to the pulse lengthof non-angled and angled injected neutral beams.

FIGS. 21A, 21B, 21C, 21D and 21E illustrate pulse length of angledinjected neutral beam and the lifetime of FRC plasma parameters ofplasma radius, plasma density, plasma temperature, and magnetic fluxcorresponding to the pulse length of angled injected neutral beams.

FIGS. 22A and 22B illustrate the basic layout of a compact toroid (CT)injector.

FIGS. 23A and 23B illustrate the central confinement vessel showing theCT injector mounted thereto.

FIGS. 24A and 24B illustrate the basic layout of an alternativeembodiment of the CT injector having a drift tube coupled thereto.

FIG. 25 illustrates a sectional isometric view of a neutral beam systemand key components for tunable energy beam output.

FIG. 26 is a schematic illustrating the neutral beam system with tunableenergy beam output.

FIG. 27 is a schematic of illustrating an axial position controlmechanism of an FRC plasma within a confining vessel (CV).

FIG. 28 is a flow diagram of a generic sliding mode control scheme.

FIG. 29 is a composite graph of examples of a sliding mode axialposition control simulation.

FIG. 30 is a composite graph of examples of a sliding mode axialposition control simulation.

It should be noted that the figures are not necessarily drawn to scaleand that elements of similar structures or functions are generallyrepresented by like reference numerals for illustrative purposesthroughout the figures. It also should be noted that the figures areonly intended to facilitate the description of the various embodimentsdescribed herein. The figures do not necessarily describe every aspectof the teachings disclosed herein and do not limit the scope of theclaims.

DETAILED DESCRIPTION

The present embodiments provided herein are directed to systems andmethods that facilitate forming and maintaining FRCs with superiorstability as well as particle, energy and flux confinement. Some of thepresent embodiments are directed to systems and methods that facilitateforming and maintaining FRCs with elevated system energies and improvedsustainment utilizing neutral beam injectors with tunable beam energycapabilities. Some of the present embodiments are also directed tosystems and methods that facilitate stability of an FRC plasma in bothradial and axial directions and axial position control of an FRC plasmaalong the symmetry axis of an FRC plasma confinement chamber independentof the axial stability properties of the FRC plasma's equilibrium.

Representative examples of the embodiments described herein, whichexamples utilize many of these additional features and teachings bothseparately and in combination, will now be described in further detailwith reference to the attached drawings. This detailed description ismerely intended to teach a person of skill in the art further detailsfor practicing preferred aspects of the present teachings and is notintended to limit the scope of the invention. Therefore, combinations offeatures and steps disclosed in the following detail description may notbe necessary to practice the invention in the broadest sense, and areinstead taught merely to particularly describe representative examplesof the present teachings.

Moreover, the various features of the representative examples and thedependent claims may be combined in ways that are not specifically andexplicitly enumerated in order to provide additional useful embodimentsof the present teachings. In addition, it is expressly noted that allfeatures disclosed in the description and/or the claims are intended tobe disclosed separately and independently from each other for thepurpose of original disclosure, as well as for the purpose ofrestricting the claimed subject matter independent of the compositionsof the features in the embodiments and/or the claims. It is alsoexpressly noted that all value ranges or indications of groups ofentities disclose every possible intermediate value or intermediateentity for the purpose of original disclosure, as well as for thepurpose of restricting the claimed subject matter.

Before turning to the systems and methods that facilitate stability ofan FRC plasma in both radial and axial directions and axial positioncontrol of an FRC plasma along the symmetry axis of an FRC plasmaconfinement chamber, a discussion of systems and methods for forming andmaintaining high performance FRCs with superior stability as well assuperior particle, energy and flux confinement over conventional FRCs isprovided. Such high performance FRCs provide a pathway to a wholevariety of applications including compact neutron sources (for medicalisotope production, nuclear waste remediation, materials research,neutron radiography and tomography), compact photon sources (forchemical production and processing), mass separation and enrichmentsystems, and reactor cores for fusion of light nuclei for the futuregeneration of energy.

Various ancillary systems and operating modes have been explored toassess whether there is a superior confinement regime in FRCs. Theseefforts have led to breakthrough discoveries and the development of aHigh Performance FRC paradigm described herein. In accordance with thisnew paradigm, the present systems and methods combine a host of novelideas and means to dramatically improve FRC confinement as illustratedin FIG. 1 as well as provide stability control without negativeside-effects. As discussed in greater detail below, FIG. 1 depictsparticle confinement in an FRC system 10 described below (see FIGS. 2and 3), operating in accordance with a High Performance FRC regime (HPF)for forming and maintaining an FRC versus operating in accordance with aconventional regime CR for forming and maintaining an FRC, and versusparticle confinement in accordance with conventional regimes for formingand maintaining an FRC used in other experiments. The present disclosurewill outline and detail the innovative individual components of the FRCsystem 10 and methods as well as their collective effects.

FRC System Vacuum System

FIGS. 2 and 3 depict a schematic of the present FRC system 10. The FRCsystem 10 includes a central confinement vessel 100 surrounded by twodiametrically opposed reversed-field-theta-pinch formation sections 200and, beyond the formation sections 200, two divertor chambers 300 tocontrol neutral density and impurity contamination. The present FRCsystem 10 was built to accommodate ultrahigh vacuum and operates attypical base pressures of 10⁻⁸ torr. Such vacuum pressures require theuse of double-pumped mating flanges between mating components, metalO-rings, high purity interior walls, as well as careful initial surfaceconditioning of all parts prior to assembly, such as physical andchemical cleaning followed by a 24 hour 250° C. vacuum baking andhydrogen glow discharge cleaning.

The reversed-field-theta-pinch formation sections 200 are standardfield-reversed-theta-pinches (FRTPs), albeit with an advanced pulsedpower formation system discussed in detail below (see FIGS. 4 through6). Each formation section 200 is made of standard opaque industrialgrade quartz tubes that feature a 2 millimeter inner lining of ultrapurequartz. The confinement chamber 100 is made of stainless steel to allowa multitude of radial and tangential ports; it also serves as a fluxconserver on the timescale of the experiments described below and limitsfast magnetic transients. Vacuums are created and maintained within theFRC system 10 with a set of dry scroll roughing pumps, turbo molecularpumps and cryo pumps.

Magnetic System

The magnetic system 400 is illustrated in FIGS. 2 and 3. FIG. 2, amongstother features, illustrates an FRC magnetic flux and density contours(as functions of the radial and axial coordinates) pertaining to an FRC450 producible by the FRC system 10. These contours were obtained by a2-D resistive Hall-MHD numerical simulation using code developed tosimulate systems and methods corresponding to the FRC system 10, andagree well with measured experimental data. As seen in FIG. 2, the FRC450 consists of a torus of closed field lines at the interior 453 of theFRC 450 inside a separatrix 451, and of an annular edge layer 456 on theopen field lines 452 just outside the separatrix 451. The edge layer 456coalesces into jets 454 beyond the FRC length, providing a naturaldivertor.

The main magnetic system 410 includes a series of quasi-dc coils 412,414, and 416 that are situated at particular axial positions along thecomponents, i.e., along the confinement chamber 100, the formationsections 200 and the divertors 300, of the FRC system 10. The quasi-dccoils 412, 414 and 416 are fed by quasi-dc switching power supplies andproduce basic magnetic bias fields of about 0.1 T in the confinementchamber 100, the formation sections 200 and the divertors 300. Inaddition to the quasi-dc coils 412, 414 and 416, the main magneticsystem 410 includes quasi-dc mirror coils 420 (fed by switchingsupplies) between either end of the confinement chamber 100 and theadjacent formation sections 200. The quasi-dc mirror coils 420 providemagnetic mirror ratios of up to 5 and can be independently energized forequilibrium shaping control. In addition, mirror plugs 440, arepositioned between each of the formation sections 200 and divertors 300.The mirror plugs 440 comprise compact quasi-dc mirror coils 430 andmirror plug coils 444. The quasi-dc mirror coils 430 include three coils432, 434 and 436 (fed by switching supplies) that produce additionalguide fields to focus the magnetic flux surfaces 455 towards the smalldiameter passage 442 passing through the mirror plug coils 444. Themirror plug coils 444, which wrap around the small diameter passage 442and are fed by LC pulsed power circuitry, produce strong magnetic mirrorfields of up to 4 T. The purpose of this entire coil arrangement is totightly bundle and guide the magnetic flux surfaces 455 andend-streaming plasma jets 454 into the remote chambers 310 of thedivertors 300. Finally, a set of saddle-coil “antennas” 460 (see FIG.15) are located outside the confinement chamber 100, two on each side ofthe mid-plane, and are fed by dc power supplies. The saddle-coilantennas 460 can be configured to provide a quasi-static magnetic dipoleor quadrupole field of about 0.01 T for controlling rotationalinstabilities and/or electron current control. The saddle-coil antennas460 can flexibly provide magnetic fields that are either symmetric orantisymmetric about the machine's midplane, depending on the directionof the applied currents.

Pulsed Power Formation Systems

The pulsed power formation systems 210 operate on a modified theta-pinchprinciple. There are two systems that each power one of the formationsections 200. FIGS. 4 through 6 illustrate the main building blocks andarrangement of the formation systems 210. The formation system 210 iscomposed of a modular pulsed power arrangement that consists ofindividual units (=skids) 220 that each energize a sub-set of coils 232of a strap assembly 230 (=straps) that wrap around the formation quartztubes 240. Each skid 220 is composed of capacitors 221, inductors 223,fast high current switches 225 and associated trigger 222 and dumpcircuitry 224. In total, each formation system 210 stores between350-400 kJ of capacitive energy, which provides up to 35 GW of power toform and accelerate the FRCs. Coordinated operation of these componentsis achieved via a state-of-the-art trigger and control system 222 and224 that allows synchronized timing between the formation systems 210 oneach formation section 200 and minimizes switching jitter to tens ofnanoseconds. The advantage of this modular design is its flexibleoperation: FRCs can be formed in-situ and then accelerated and injected(=static formation) or formed and accelerated at the same time (=dynamicformation).

Neutral Beam Injectors

Neutral atom beams 600 are deployed on the FRC system 10 to provideheating and current drive as well as to develop fast particle pressure.As shown in FIGS. 3A, 3B and 8, the individual beam lines comprisingneutral atom beam injector systems 610 and 640 are located around thecentral confinement chamber 100 and inject fast particles tangentiallyto the FRC plasma (and perpendicular or at an angel normal to the majoraxis of symmetry in the central confinement vessel 100) with an impactparameter such that the target trapping zone lies well within theseparatrix 451 (see FIG. 2). Each injector system 610 and 640 is capableof injecting up to 1 MW of neutral beam power into the FRC plasma withparticle energies between 20 and 40 keV. The systems 610 and 640 arebased on positive ion multi-aperture extraction sources and utilizegeometric focusing, inertial cooling of the ion extraction grids anddifferential pumping. Apart from using different plasma sources, thesystems 610 and 640 are primarily differentiated by their physicaldesign to meet their respective mounting locations, yielding side andtop injection capabilities. Typical components of these neutral beaminjectors are specifically illustrated in FIG. 7 for the side injectorsystems 610. As shown in FIG. 7, each individual neutral beam system 610includes an RF plasma source 612 at an input end (this is substitutedwith an arc source in systems 640) with a magnetic screen 614 coveringthe end. An ion optical source and acceleration grids 616 is coupled tothe plasma source 612 and a gate valve 620 is positioned between the ionoptical source and acceleration grids 616 and a neutralizer 622. Adeflection magnet 624 and an ion dump 628 are located between theneutralizer 622 and an aiming device 630 at the exit end. A coolingsystem comprises two cryo-refrigerators 634, two cryopanels 636 and aLN2 shroud 638. This flexible design allows for operation over a broadrange of FRC parameters.

An alternative configuration for the neutral atom beam injectors 600 isthat of injecting the fast particles tangentially to the FRC plasma, butwith an angle A less than 90° relative to the major axis of symmetry inthe central confinement vessel 100. These types of orientation of thebeam injectors 615 are shown in FIG. 3C. In addition, the beam injectors615 may be oriented such that the beam injectors 615 on either side ofthe mid-plane of the central confinement vessel 100 inject theirparticles towards the mid-plane. Finally, the axial position of thesebeam systems 600 may be chosen closer to the mid-plane. Thesealternative injection embodiments facilitate a more central fuelingoption, which provides for better coupling of the beams and highertrapping efficiency of the injected fast particles. Furthermore,depending on the angle and axial position, this arrangement of the beaminjectors 615 allows more direct and independent control of the axialelongation and other characteristics of the FRC 450. For instance,injecting the beams at a shallow angle A relative to the vessel's majoraxis of symmetry will create an FRC plasma with longer axial extensionand lower temperature while picking a more perpendicular angle A willlead to an axially shorter but hotter plasma. In this fashion theinjection angle A and location of the beam injectors 615 can beoptimized for different purposes. In addition, such angling andpositioning of the beam injectors 615 can allow beams of higher energy(which is generally more favorable for depositing more power with lessbeam divergence) to be injected into lower magnetic fields than wouldotherwise be necessary to trap such beams. This is due to the fact thatit is the azimuthal component of the energy that determines fast ionorbit scale (which becomes progressively smaller as the injection anglerelative to the vessel's major axis of symmetry is reduced at constantbeam energy). Furthermore, angled injection towards the mid-plane andwith axial beam positions close to the mid-plane improves beam-plasmacoupling, even as the FRC plasma shrinks or otherwise axially contractsduring the injection period.

Turning to FIGS. 3D and 3E, another alternative configuration of the FRCsystem 10 includes inner divertors 302 in addition to the angled beaminjectors 615. The inner divertors 302 are positioned between theformation sections 200 and the confinement chamber 100, and areconfigured and operate substantially similar to the outer divertors 300.The inner divertors 302, which include fast switching magnetic coilstherein, are effectively inactive during the formation process to enablethe formation FRCs to pass through the inner divertors 302 as theformation FRCs translate toward the mid-plane of the confinement chamber100. Once the formation FRCs pass through the inner divertors 302 intothe confinement chamber 100, the inner divertors are activated tooperate substantially similar to the outer divertors and isolate theconfinement chamber 100 from the formation sections 200.

Pellet Injector

To provide a means to inject new particles and better control FRCparticle inventory, a 12-barrel pellet injector 700 (see e.g. I. Vinyaret al., “Pellet Injectors Developed at PELIN for JET, TAE, and HL-2A,”Proceedings of the 26^(th) Fusion Science and Technology Symposium,09/27 to 10/01 (2010)) is utilized on FRC system 10. FIG. 3 illustratesthe layout of the pellet injector 700 on the FRC system 10. Thecylindrical pellets (D˜1 mm, L˜1-2 mm) are injected into the FRC with avelocity in the range of 150-250 km/s. Each individual pellet containsabout 5×10¹⁹ hydrogen atoms, which is comparable to the FRC particleinventory.

Gettering Systems

It is well known that neutral halo gas is a serious problem in allconfinement systems. The charge exchange and recycling (release of coldimpurity material from the wall) processes can have a devastating effecton energy and particle confinement. In addition, any significant densityof neutral gas at or near the edge will lead to prompt losses of or atleast severely curtail the lifetime of injected large orbit (highenergy) particles (large orbit refers to particles having orbits on thescale of the FRC topology or at least orbit radii much larger than thecharacteristic magnetic field gradient length scale)—a fact that isdetrimental to all energetic plasma applications, including fusion viaauxiliary beam heating.

Surface conditioning is a means by which the detrimental effects ofneutral gas and impurities can be controlled or reduced in a confinementsystem. To this end the FRC system 10 provided herein employs Titaniumand Lithium deposition systems 810 and 820 that coat the plasma facingsurfaces of the confinement chamber (or vessel) 100 and divertors 300and 302 with films (tens of micrometers thick) of Ti and/or Li. Thecoatings are achieved via vapor deposition techniques. Solid Li and/orTi are evaporated and/or sublimated and sprayed onto nearby surfaces toform the coatings. The sources are atomic ovens with guide nozzles (incase of Li) 822 or heated spheres of solid with guide shrouding (in caseof Ti) 812. Li evaporator systems typically operate in a continuous modewhile Ti sublimators are mostly operated intermittently in betweenplasma operation. Operating temperatures of these systems are above 600°C. to obtain fast deposition rates. To achieve good wall coverage,multiple strategically located evaporator/sublimator systems arenecessary. FIG. 9 details a preferred arrangement of the getteringdeposition systems 810 and 820 in the FRC system 10. The coatings act asgettering surfaces and effectively pump atomic and molecular hydrogenicspecies (H and D). The coatings also reduce other typical impuritiessuch as Carbon and Oxygen to insignificant levels.

Mirror Plugs

As stated above, the FRC system 10 employs sets of mirror coils 420,430, and 444 as shown in FIGS. 2 and 3. A first set of mirror coils 420is located at the two axial ends of the confinement chamber 100 and isindependently energized from the DC confinement, formation and divertorcoils 412, 414 and 416 of the main magnetic system 410. The first set ofmirror coils 420 primarily helps to steer and axially contain the FRC450 during merging and provides equilibrium shaping control duringsustainment. The first mirror coil set 420 produces nominally highermagnetic fields (around 0.4 to 0.5 T) than the central confinement fieldproduced by the central confinement coils 412. The second set of mirrorcoils 430, which includes three compact quasi-dc mirror coils 432, 434and 436, is located between the formation sections 200 and the divertors300 and are driven by a common switching power supply. The mirror coils432, 434 and 436, together with the more compact pulsed mirror plugcoils 444 (fed by a capacitive power supply) and the physicalconstriction 442 form the mirror plugs 440 that provide a narrow low gasconductance path with very high magnetic fields (between 2 to 4 T withrise times of about 10 to 20 ms). The most compact pulsed mirror coils444 are of compact radial dimensions, bore of 20 cm and similar length,compared to the meter-plus-scale bore and pancake design of theconfinement coils 412, 414 and 416. The purpose of the mirror plugs 440is multifold: (1) The coils 432, 434, 436 and 444 tightly bundle andguide the magnetic flux surfaces 452 and end-streaming plasma jets 454into the remote divertor chambers 300. This assures that the exhaustparticles reach the divertors 300 appropriately and that there arecontinuous flux surfaces 455 that trace from the open field line 452region of the central FRC 450 all the way to the divertors 300. (2) Thephysical constrictions 442 in the FRC system 10, through which that thecoils 432, 434, 436 and 444 enable passage of the magnetic flux surfaces452 and plasma jets 454, provide an impediment to neutral gas flow fromthe plasma guns 350 that sit in the divertors 300. In the same vein, theconstrictions 442 prevent back-streaming of gas from the formationsections 200 to the divertors 300 thereby reducing the number of neutralparticles that has to be introduced into the entire FRC system 10 whencommencing the startup of an FRC. (3) The strong axial mirrors producedby the coils 432, 434, 436 and 444 reduce axial particle losses andthereby reduce the parallel particle diffusivity on open field lines.

In the alternative configuration shown in FIGS. 3D and 3E, a set of lowprofile necking coils 421 are positions between the inner divertors 302and the formations sections 200.

Axial Plasma Guns

Plasma streams from guns 350 mounted in the divertor chambers 310 of thedivertors 300 are intended to improve stability and neutral beamperformance. The guns 350 are mounted on axis inside the chamber 310 ofthe divertors 300 as illustrated in FIGS. 3 and 10 and produce plasmaflowing along the open flux lines 452 in the divertor 300 and towardsthe center of the confinement chamber 100. The guns 350 operate at ahigh density gas discharge in a washer-stack channel and are designed togenerate several kiloamperes of fully ionized plasma for 5 to 10 ms. Theguns 350 include a pulsed magnetic coil that matches the output plasmastream with the desired size of the plasma in the confinement chamber100. The technical parameters of the guns 350 are characterized by achannel having a 5 to 13 cm outer diameter and up to about 10 cm innerdiameter and provide a discharge current of 10-15 kA at 400-600 V with agun-internal magnetic field of between 0.5 to 2.3 T.

The gun plasma streams can penetrate the magnetic fields of the mirrorplugs 440 and flow into the formation section 200 and confinementchamber 100. The efficiency of plasma transfer through the mirror plug440 increases with decreasing distance between the gun 350 and the plug440 and by making the plug 440 wider and shorter. Under reasonableconditions, the guns 350 can each deliver approximately 10²² protons/sthrough the 2 to 4 T mirror plugs 440 with high ion and electrontemperatures of about 150 to 300 eV and about 40 to 50 eV, respectively.The guns 350 provide significant refueling of the FRC edge layer 456,and an improved overall FRC particle confinement.

To further increase the plasma density, a gas box could be utilized topuff additional gas into the plasma stream from the guns 350. Thistechnique allows a several-fold increase in the injected plasma density.In the FRC system 10, a gas box installed on the divertor 300 side ofthe mirror plugs 440 improves the refueling of the FRC edge layer 456,formation of the FRC 450, and plasma line-tying.

Given all the adjustment parameters discussed above and also taking intoaccount that operation with just one or both guns is possible, it isreadily apparent that a wide spectrum of operating modes is accessible.

Biasing Electrodes

Electrical biasing of open flux surfaces can provide radial potentialsthat give rise to azimuthal EXB motion that provides a controlmechanism, analogous to turning a knob, to control rotation of the openfield line plasma as well as the actual FRC core 450 via velocity shear.To accomplish this control, the FRC system 10 employs various electrodesstrategically placed in various parts of the machine. FIG. 3 depictsbiasing electrodes positioned at preferred locations within the FRCsystem 10.

In principle, there are 4 classes of elctrodes: (1) point electrodes 905in the confinement chamber 100 that make contact with particular openfield lines 452 in the edge of the FRC 450 to provide local charging,(2) annular electrodes 900 between the confinement chamber 100 and theformation sections 200 to charge far-edge flux layers 456 in anazimuthally symmetric fashion, (3) stacks of concentric electrodes 910in the divertors 300 to charge multiple concentric flux layers 455(whereby the selection of layers is controllable by adjusting coils 416to adjust the divertor magnetic field so as to terminate the desiredflux layers 456 on the appropriate electrodes 910), and finally (4) theanodes 920 (see FIG. 10) of the plasma guns 350 themselves (whichintercept inner open flux surfaces 455 near the separatrix of the FRC450). FIGS. 10 and 11 show some typical designs for some of these.

In all cases these electrodes are driven by pulsed or dc power sourcesat voltages up to about 800 V. Depending on electrode size and what fluxsurfaces are intersected, currents can be drawn in the kilo-ampererange.

Un-Sustained Operation of FRC System—Conventional Regime

The standard plasma formation on the FRC system 10 follows thewell-developed reversed-field-theta-pinch technique. A typical processfor starting up an FRC commences by driving the quasi-dc coils 412, 414,416, 420, 432, 434 and 436 to steady state operation. The RFTP pulsedpower circuits of the pulsed power formation systems 210 then drive thepulsed fast reversed magnet field coils 232 to create a temporaryreversed bias of about −0.05 T in the formation sections 200. At thispoint a predetermined amount of neutral gas at 9-20 psi is injected intothe two formation volumes defined by the quartz-tube chambers 240 of the(north and south) formation sections 200 via a set ofazimuthally-oriented puff-vales at flanges located on the outer ends ofthe formation sections 200. Next a small RF (˜hundreds of kilo-hertz)field is generated from a set of antennas on the surface of the quartztubes 240 to create pre-ionization in the form of local seed ionizationregions within the neutral gas columns. This is followed by applying atheta-ringing modulation on the current driving the pulsed fast reversedmagnet field coils 232, which leads to more global pre-ionization of thegas columns. Finally, the main pulsed power banks of the pulsed powerformation systems 210 are fired to drive pulsed fast reversed magnetfield coils 232 to create a forward-biased field of up to 0.4 T. Thisstep can be time-sequenced such that the forward-biased field isgenerated uniformly throughout the length of the formation tubes 240(static formation) or such that a consecutive peristaltic fieldmodulation is achieved along the axis of the formation tubes 240(dynamic formation).

In this entire formation process, the actual field reversal in theplasma occurs rapidly, within about 5 μs. The multi-gigawatt pulsedpower delivered to the forming plasma readily produces hot FRCs whichare then ejected from the formation sections 200 via application ofeither a time-sequenced modulation of the forward magnetic field(magnetic peristalsis) or temporarily increased currents in the lastcoils of coil sets 232 near the axial outer ends of the formation tubes210 (forming an axial magnetic field gradient that points axiallytowards the confinement chamber 100). The two (north and south)formation FRCs so formed and accelerated then expand into the largerdiameter confinement chamber 100, where the quasi-dc coils 412 produce aforward-biased field to control radial expansion and provide theequilibrium external magnetic flux.

Once the north and south formation FRCs arrive near the midplane of theconfinement chamber 100, the FRCs collide. During the collision theaxial kinetic energies of the north and south formation FRCs are largelythermalized as the FRCs merge ultimately into a single FRC 450. A largeset of plasma diagnostics are available in the confinement chamber 100to study the equilibria of the FRC 450. Typical operating conditions inthe FRC system 10 produce compound FRCs with separatrix radii of about0.4 m and about 3 m axial extend. Further characteristics are externalmagnetic fields of about 0.1 T, plasma densities around 5×10¹⁹ m⁻³ andtotal plasma temperature of up to 1 keV. Without any sustainment, i.e.,no heating and/or current drive via neutral beam injection or otherauxiliary means, the lifetime of these FRCs is limited to about 1 ms,the indigenous characteristic configuration decay time.

Experimental Data of Unsustained Operation—Conventional Regime

FIG. 12 shows a typical time evolution of the excluded flux radius,r_(ΔΦ), which approximates the separatrix radius, r_(s), to illustratethe dynamics of the theta-pinch merging process of the FRC 450. The two(north and south) individual plasmoids are produced simultaneously andthen accelerated out of the respective formation sections 200 at asupersonic speed, v_(Z)˜250 km/s, and collide near the midplane at z=0.During the collision the plasmoids compress axially, followed by a rapidradial and axial expansion, before eventually merging to form an FRC450. Both radial and axial dynamics of the merging FRC 450 are evidencedby detailed density profile measurements and bolometer-based tomography.

Data from a representative un-sustained discharge of the FRC system 10are shown as functions of time in FIGS. 13A, 13B, 13C and 13D. The FRCis initiated at t=0. The excluded flux radius at the machine's axialmid-plane is shown in FIG. 13A. This data is obtained from an array ofmagnetic probes, located just inside the confinement chamber's stainlesssteel wall, that measure the axial magnetic field. The steel wall is agood flux conserver on the time scales of this discharge.

Line-integrated densities are shown in FIG. 13B, from a 6-chordCO₂/He—Ne interferometer located at z=0. Taking into account vertical(y) FRC displacement, as measured by bolometric tomography, Abelinversion yields the density contours of FIGS. 13C. After some axial andradial sloshing during the first 0.1 ms, the FRC settles with a hollowdensity profile. This profile is fairly flat, with substantial densityon axis, as required by typical 2-D FRC equilibria.

Total plasma temperature is shown in FIG. 13D, derived from pressurebalance and fully consistent with Thomson scattering and spectroscopymeasurements.

Analysis from the entire excluded flux array indicates that the shape ofthe FRC separatrix (approximated by the excluded flux axial profiles)evolves gradually from racetrack to elliptical. This evolution, shown inFIG. 14, is consistent with a gradual magnetic reconnection from two toa single FRC. Indeed, rough estimates suggest that in this particularinstant about 10% of the two initial FRC magnetic fluxes reconnectsduring the collision.

The FRC length shrinks steadily from 3 down to about 1 m during the FRClifetime. This shrinkage, visible in FIG. 14, suggests that mostlyconvective energy loss dominates the FRC confinement. As the plasmapressure inside the separatrix decreases faster than the externalmagnetic pressure, the magnetic field line tension in the end regionscompresses the FRC axially, restoring axial and radial equilibrium. Forthe discharge discussed in FIGS. 13 and 14, the FRC magnetic flux,particle inventory, and thermal energy (about 10 mWb, 7×10¹⁹ particles,and 7 kJ, respectively) decrease by roughly an order of magnitude in thefirst millisecond, when the FRC equilibrium appears to subside.

Sustained Operation—HPF Regime

The examples in FIGS. 12 to 14 are characteristic of decaying FRCswithout any sustainment. However, several techniques are deployed on theFRC system 10 to further improve FRC confinement (inner core and edgelayer) to the HPF regime and sustain the configuration.

Neutral Beams

First, fast (H) neutrals are injected perpendicular to B_(z) in beamsfrom the eight neutral beam injectors 600. The beams of fast neutralsare injected from the moment the north and south formation FRCs merge inthe confinement chamber 100 into one FRC 450. The fast ions, createdprimarily by charge exchange, have betatron orbits (with primary radiion the scale of the FRC topology or at least much larger than thecharacteristic magnetic field gradient length scale) that add to theazimuthal current of the FRC 450. After some fraction of the discharge(after 0.5 to 0.8 ms into the shot), a sufficiently large fast ionpopulation significantly improves the inner FRC's stability andconfinement properties (see e.g. M. W. Binderbauer and N. Rostoker,Plasma Phys. 56, part 3, 451 (1996)). Furthermore, from a sustainmentperspective, the beams from the neutral beam injectors 600 are also theprimary means to drive current and heat the FRC plasma.

In the plasma regime of the FRC system 10, the fast ions slow downprimarily on plasma electrons. During the early part of a discharge,typical orbit-averaged slowing-down times of fast ions are 0.3-0.5 ms,which results in significant FRC heating, primarily of electrons. Thefast ions make large radial excursions outside of the separatrix becausethe internal FRC magnetic field is inherently low (about 0.03 T onaverage for a 0.1 T external axial field). The fast ions would bevulnerable to charge exchange loss, if the neutral gas density were toohigh outside of the separatrix. Therefore, wall gettering and othertechniques (such as the plasma gun 350 and mirror plugs 440 thatcontribute, amongst other things, to gas control) deployed on the FRCsystem 10 tend to minimize edge neutrals and enable the requiredbuild-up of fast ion current.

Pellet Injection

When a significant fast ion population is built up within the FRC 450,with higher electron temperatures and longer FRC lifetimes, frozen H orD pellets are injected into the FRC 450 from the pellet injector 700 tosustain the FRC particle inventory of the FRC 450. The anticipatedablation timescales are sufficiently short to provide a significant FRCparticle source. This rate can also be increased by enlarging thesurface area of the injected piece by breaking the individual pelletinto smaller fragments while in the barrels or injection tubes of thepellet injector 700 and before entering the confinement chamber 100, astep that can be achieved by increasing the friction between the pelletand the walls of the injection tube by tightening the bend radius of thelast segment of the injection tube right before entry into theconfinement chamber 100. By virtue of varying the firing sequence andrate of the 12 barrels (injection tubes) as well as the fragmentation,it is possible to tune the pellet injection system 700 to provide justthe desired level of particle inventory sustainment. In turn, this helpsmaintain the internal kinetic pressure in the FRC 450 and sustainedoperation and lifetime of the FRC 450.

Once the ablated atoms encounter significant plasma in the FRC 450, theybecome fully ionized. The resultant cold plasma component is thencollisionally heated by the indigenous FRC plasma. The energy necessaryto maintain a desired FRC temperature is ultimately supplied by the beaminjectors 600. In this sense the pellet injectors 700 together with theneutral beam injectors 600 form the system that maintains a steady stateand sustains the FRC 450.

CT Injector

As an alternative to the pellet injector, a compact toroid (CT) injectoris provided, mainly for fueling field-reversed configuration (FRCs)plasmas. The CT injector 720 comprises a magnetized coaxial plasma-gun(MCPG), which, as shown in FIGS. 22A and 22B, includes coaxialcylindrical inner and outer electrodes 722 and 724, a bias coilpositioned internal to the inner electrode 726 and an electrical break728 on an end opposite the discharge of the CT injector 720. Gas isinjected through a gas injection port 730 into a space between the innerand outer electrodes 722 and 724 and a Spheromak-like plasma isgenerated therefrom by discharge and pushed out from the gun by Lorentzforce. As shown in FIGS. 23A and 23B, a pair of CT injectors 720 arecoupled to the confinement vessel 100 near and on opposition sides ofthe mid-plane of the vessel 100 to inject CTs into the central FRCplasma within the confinement vessel 100. The discharge end of the CTinjectors 720 are directed towards the mid-plane of the confinementvessel 100 at an angel to the longitudinal axis of the confinementvessel 100 similar to the neutral beam injectors 615.

In an alternative embodiment, the CT injector 720, as shown in FIGS. 24Aand 24B, include a drift tube 740 comprising an elongate cylindricaltube coupled to the discharge end of the CT injector 720. As depicted,the drift tube 740 includes drift tube coils 742 positioned about andaxially spaced along the tube. A plurality of diagnostic ports 744 aredepicted along the length of the tube.

The advantages of the CT injector 720 are: (1) control and adjustabilityof particle inventory per injected CT; (2) warm plasma is deposited(instead of cryogenic pellets); (3) system can be operated in rep-ratemode so as to allow for continuous fueling; (4) the system can alsorestore some magnetic flux as the injected CTs carry embedded magneticfield. In an embodiment for experimental use, the inner diameter of anouter electrode is 83.1 mm and the outer diameter of an inner electrodeis 54.0 mm. The surface of the inner electrode 722 is preferably coatedwith tungsten in order to reduce impurities coming out from theelectrode 722. As depicted, the bias coil 726 is mounted inside of theinner electrode 722.

In recent experiments a supersonic CT translation speed of up to ˜100km/s was achieved. Other typical plasma parameters are as follows:electron density ˜5×1021 m−3, electron temperature ˜30-50 eV, andparticle inventory of ˜0.5-1.0×1019. The high kinetic pressure of the CTallows the injected plasma to penetrate deeply into the FRC and depositthe particles inside the separatrix. In recent experiments FRC particlefueling has resulted in ˜10-20% of the FRC particle inventory beingprovide by the CT injectors successfully demonstrating fueling canreadily be carried out without disrupting the FRC plasma.

Saddle Coils

To achieve steady state current drive and maintain the required ioncurrent it is desirable to prevent or significantly reduce electron spinup due to the electron-ion frictional force (resulting from collisionalion electron momentum transfer). The FRC system 10 utilizes aninnovative technique to provide electron breaking via an externallyapplied static magnetic dipole or quadrupole field. This is accomplishedvia the external saddle coils 460 depicted in FIG. 15. The transverseapplied radial magnetic field from the saddle coils 460 induces an axialelectric field in the rotating FRC plasma. The resultant axial electroncurrent interacts with the radial magnetic field to produce an azimuthalbreaking force on the electrons, F_(θ)=−σV_(eθ)<|B_(r)|²>. For typicalconditions in the FRC system 10, the required applied magnetic dipole(or quadrupole) field inside the plasma needs to be only of order 0.001T to provide adequate electron breaking. The corresponding externalfield of about 0.015 T is small enough to not cause appreciable fastparticle losses or otherwise negatively impact confinement. In fact, theapplied magnetic dipole (or quadrupole) field contributes to suppressinstabilities. In combination with tangential neutral beam injection andaxial plasma injection, the saddle coils 460 provide an additional levelof control with regards to current maintenance and stability.

Mirror Plugs

The design of the pulsed coils 444 within the mirror plugs 440 permitsthe local generation of high magnetic fields (2 to 4 T) with modest(about 100 kJ) capacitive energy. For formation of magnetic fieldstypical of the present operation of the FRC system 10, all field lineswithin the formation volume are passing through the constrictions 442 atthe mirror plugs 440, as suggested by the magnetic field lines in FIG. 2and plasma wall contact does not occur. Furthermore, the mirror plugs440 in tandem with the quasi-dc divertor magnets 416 can be adjusted soto guide the field lines onto the divertor electrodes 910, or flare thefield lines in an end cusp configuration (not shown). The latterimproves stability and suppresses parallel electron thermal conduction.

The mirror plugs 440 by themselves also contribute to neutral gascontrol. The mirror plugs 440 permit a better utilization of thedeuterium gas puffed in to the quartz tubes during FRC formation, as gasback-streaming into the divertors 300 is significantly reduced by thesmall gas conductance of the plugs (a meager 500 L/s). Most of theresidual puffed gas inside the formation tubes 210 is quickly ionized.In addition, the high-density plasma flowing through the mirror plugs440 provides efficient neutral ionization hence an effective gasbarrier. As a result, most of the neutrals recycled in the divertors 300from the FRC edge layer 456 do not return to the confinement chamber100. In addition, the neutrals associated with the operation of theplasma guns 350 (as discussed below) will be mostly confined to thedivertors 300.

Finally, the mirror plugs 440 tend to improve the FRC edge layerconfinement. With mirror ratios (plug/confinement magnetic fields) inthe range 20 to 40, and with a 15 m length between the north and southmirror plugs 440, the edge layer particle confinement time τ_(∥)increases by up to an order of magnitude. Improving τ_(∥) readilyincreases the FRC particle confinement.

Assuming radial diffusive (D) particle loss from the separatrix volume453 balanced by axial loss (τ_(∥)) from the edge layer 456, one obtains(2πr_(s)L_(s))(Dn_(s)/δ)=(2πr_(s)L_(s)δ)(n_(s)/τ_(∥)), from which theseparatrix density gradient length can be rewritten as δ=(Dτ_(∥))^(1/2).Here r_(s), L_(s) and n_(s) are separatrix radius, separatrix length andseparatrix density, respectively. The FRC particle confinement time isτ_(N)=[πr_(s)²L_(s)<n>]/[(2πr_(s)L_(s))(Dn_(s)/δ)]=(<n>/n_(s))(τ_(⊥)τ_(∥))^(1/2),where τ_(⊥)=a²/D with a=r_(s)/4. Physically, improving τ_(∥) leads toincreased δ (reduced separatrix density gradient and drift parameter),and, therefore, reduced FRC particle loss. The overall improvement inFRC particle confinement is generally somewhat less than quadraticbecause n_(s) increases with τ_(∥).

A significant improvement in τ_(∥) also requires that the edge layer 456remains grossly stable (i.e., no n=1 flute, firehose, or other MHDinstability typical of open systems). Use of the plasma guns 350provides for this preferred edge stability. In this sense, the mirrorplugs 440 and plasma gun 350 form an effective edge control system.

Plasma Guns

The plasma guns 350 improve the stability of the FRC exhaust jets 454 byline-tying. The gun plasmas from the plasma guns 350 are generatedwithout azimuthal angular momentum, which proves useful in controllingFRC rotational instabilities. As such the guns 350 are an effectivemeans to control FRC stability without the need for the older quadrupolestabilization technique. As a result, the plasma guns 350 make itpossible to take advantage of the beneficial effects of fast particlesor access the advanced hybrid kinetic FRC regime as outlined in thisdisclosure. Therefore, the plasma guns 350 enable the FRC system 10 tobe operated with saddle coil currents just adequate for electronbreaking but below the threshold that would cause FRC instability and/orlead to dramatic fast particle diffusion.

As mentioned in the Mirror Plug discussion above, if τ_(∥) can besignificantly improved, the supplied gun plasma would be comparable tothe edge layer particle loss rate (˜10²²/s). The lifetime of thegun-produced plasma in the FRC system 10 is in the millisecond range.Indeed, consider the gun plasma with density n_(e)˜10¹³ cm⁻³ and iontemperature of about 200 eV, confined between the end mirror plugs 440.The trap length L and mirror ratio R are about 15 m and 20,respectively. The ion mean free path due to Coulomb collisions isλ_(ii)˜6×10³ cm and, since λ_(ii)InR/R<L, the ions are confined in thegas-dynamic regime. The plasma confinement time in this regime isτ_(gd)˜RL/2V_(s)˜2 ms, where V_(s) is the ion sound speed. Forcomparison, the classical ion confinement time for these plasmaparameters would be τ_(c)˜0.5τ_(ii)(ln R+(ln R)^(0.5))˜0.7 ms. Theanomalous transverse diffusion may, in principle, shorten the plasmaconfinement time. However, in the FRC system 10, if we assume the Bohmdiffusion rate, the estimated transverse confinement time for the gunplasma is τ_(⊥)>τ_(gd)˜2 ms. Hence, the guns would provide significantrefueling of the FRC edge layer 456, and an improved overall FRCparticle confinement.

Furthermore, the gun plasma streams can be turned on in about 150 to 200microseconds, which permits use in FRC start-up, translation, andmerging into the confinement chamber 100. If turned on around t˜0 (FRCmain bank initiation), the gun plasmas help to sustain the presentdynamically formed and merged FRC 450. The combined particle inventoriesfrom the formation FRCs and from the guns is adequate for neutral beamcapture, plasma heating, and long sustainment. If turned on at tin therange −1 to 0 ms, the gun plasmas can fill the quartz tubes 210 withplasma or ionize the gas puffed into the quartz tubes, thus permittingFRC formation with reduced or even perhaps zero puffed gas. The lattermay require sufficiently cold formation plasma to permit fast diffusionof the reversed bias magnetic field. If turned on at t<−2 ms, the plasmastreams could fill the about 1 to 3 m³ field line volume of theformation and confinement regions of the formation sections 200 andconfinement chamber 100 with a target plasma density of a few 10¹³ cm⁻³,sufficient to allow neutral beam build-up prior to FRC arrival. Theformation FRCs could then be formed and translated into the resultingconfinement vessel plasma. In this way the plasma guns 350 enable a widevariety of operating conditions and parameter regimes.

Electrical Biasing

Control of the radial electric field profile in the edge layer 456 isbeneficial in various ways to FRC stability and confinement. By virtueof the innovative biasing components deployed in the FRC system 10 it ispossible to apply a variety of deliberate distributions of electricpotentials to a group of open flux surfaces throughout the machine fromareas well outside the central confinement region in the confinementchamber 100. In this way radial electric fields can be generated acrossthe edge layer 456 just outside of the FRC 450. These radial electricfields then modify the azimuthal rotation of the edge layer 456 andeffect its confinement via E×B velocity shear. Any differential rotationbetween the edge layer 456 and the FRC core 453 can then be transmittedto the inside of the FRC plasma by shear. As a result, controlling theedge layer 456 directly impacts the FRC core 453. Furthermore, since thefree energy in the plasma rotation can also be responsible forinstabilities, this technique provides a direct means to control theonset and growth of instabilities. In the FRC system 10, appropriateedge biasing provides an effective control of open field line transportand rotation as well as FRC core rotation. The location and shape of thevarious provided electrodes 900, 905, 910 and 920 allows for control ofdifferent groups of flux surfaces 455 and at different and independentpotentials. In this way a wide array of different electric fieldconfigurations and strengths can be realized, each with differentcharacteristic impact on plasma performance.

A key advantage of all these innovative biasing techniques is the factthat core and edge plasma behavior can be affected from well outside theFRC plasma, i.e. there is no need to bring any physical components intouch with the central hot plasma (which would have severe implicationsfor energy, flux and particle losses). This has a major beneficialimpact on performance and all potential applications of the HPF concept.

Experimental Data—HPF Operation

Injection of fast particles via beams from the neutral beam guns 600plays an important role in enabling the HPF regime. FIGS. 16A, 16B, 16Cand 16D illustrate this fact. Depicted is a set of curves showing howthe FRC lifetime correlates with the length of the beam pulses. Allother operating conditions are held constant for all dischargescomprising this study. The data is averaged over many shots and,therefore, represents typical behavior. It is clearly evident thatlonger beam duration produces longer lived FRCs. Looking at thisevidence as well as other diagnostics during this study, it demonstratesthat beams increase stability and reduce losses. The correlation betweenbeam pulse length and FRC lifetime is not perfect as beam trappingbecomes inefficient below a certain plasma size, i.e., as the FRC 450shrinks in physical size not all of the injected beams are interceptedand trapped. Shrinkage of the FRC is primarily due to the fact that netenergy loss (˜4 MW about midway through the discharge) from the FRCplasma during the discharge is somewhat larger than the total power fedinto the FRC via the neutral beams (˜2.5 MW) for the particularexperimental setup. Locating the beams at a location closer to themid-plane of the vessel 100 would tend to reduce these losses and extendFRC lifetime.

FIGS. 17A, 17B, 17C and 17D illustrate the effects of differentcomponents to achieve the HPF regime. It shows a family of typicalcurves depicting the lifetime of the FRC 450 as a function of time. Inall cases a constant, modest amount of beam power (about 2.5 MW) isinjected for the full duration of each discharge. Each curve isrepresentative of a different combination of components. For example,operating the FRC system 10 without any mirror plugs 440, plasma guns350 or gettering from the gettering systems 800 results in rapid onsetof rotational instability and loss of the FRC topology. Adding only themirror plugs 440 delays the onset of instabilities and increasesconfinement. Utilizing the combination of mirror plugs 440 and a plasmagun 350 further reduces instabilities and increases FRC lifetime.Finally adding gettering (Ti in this case) on top of the gun 350 andplugs 440 yields the best results—the resultant FRC is free ofinstabilities and exhibits the longest lifetime. It is clear from thisexperimental demonstration that the full combination of componentsproduces the best effect and provides the beams with the best targetconditions.

As shown in FIG. 1, the newly discovered HPF regime exhibitsdramatically improved transport behavior. FIG. 1 illustrates the changein particle confinement time in the FRC system 10 between theconventionally regime and the HPF regime. As can be seen, it hasimproved by well over a factor of 5 in the HPF regime. In addition, FIG.1 details the particle confinement time in the FRC system 10 relative tothe particle confinement time in prior conventional FRC experiments.With regards to these other machines, the HPF regime of the FRC system10 has improved confinement by a factor of between 5 and close to 20.Finally, and most importantly, the nature of the confinement scaling ofthe FRC system 10 in the HPF regime is dramatically different from allprior measurements. Before the establishment of the HPF regime in theFRC system 10, various empirical scaling laws were derived from data topredict confinement times in prior FRC experiments. All those scalingrules depend mostly on the ratio R²/ρ_(i), where R is the radius of themagnetic field null (a loose measure of the physical scale of themachine) and ρ_(i) is the ion larmor radius evaluated in the externallyapplied field (a loose measure of the applied magnetic field). It isclear from FIG. 1 that long confinement in conventional FRCs is onlypossible at large machine size and/or high magnetic field. Operating theFRC system 10 in the conventional FRC regime CR tends to follow thosescaling rules, as indicated in FIG. 1. However, the HPF regime is vastlysuperior and shows that much better confinement is attainable withoutlarge machine size or high magnetic fields. More importantly, it is alsoclear from FIG. 1 that the HPF regime results in improved confinementtime with reduced plasma size as compared to the CR regime. Similartrends are also visible for flux and energy confinement times, asdescribed below, which have increased by over a factor of 3-8 in the FRCsystem 10 as well. The breakthrough of the HPF regime, therefore,enables the use of modest beam power, lower magnetic fields and smallersize to sustain and maintain FRC equilibria in the FRC system 10 andfuture higher energy machines. Hand-in-hand with these improvementscomes lower operating and construction costs as well as reducedengineering complexity.

For further comparison, FIGS. 18A, 18B, 18C and 18D show data from arepresentative HPF regime discharge in the FRC system 10 as a functionof time. FIG. 18A depicts the excluded flux radius at the mid-plane. Forthese longer timescales the conducting steel wall is no longer as good aflux conserver and the magnetic probes internal to the wall areaugmented with probes outside the wall to properly account for magneticflux diffusion through the steel. Compared to typical performance in theconventional regime CR, as shown in FIGS. 13A, 13B, 13C and 13D, the HPFregime operating mode exhibits over 400% longer lifetime.

A representative cord of the line integrated density trace is shown inFIG. 18B with its Abel inverted complement, the density contours, inFIG. 18C. Compared to the conventional FRC regime CR, as shown in FIGS.13A, 13B, 13C and 13D, the plasma is more quiescent throughout thepulse, indicative of very stable operation. The peak density is alsoslightly lower in HPF shots—this is a consequence of the hotter totalplasma temperature (up to a factor of 2) as shown in FIG. 18D.

For the respective discharge illustrated in FIGS. 18A, 18B, 18C and 18D,the energy, particle and flux confinement times are 0.5 ms, 1 ms and 1ms, respectively. At a reference time of 1 ms into the discharge, thestored plasma energy is 2 kJ while the losses are about 4 MW, makingthis target very suitable for neutral beam sustainment.

FIG. 19 summarizes all advantages of the HPF regime in the form of anewly established experimental HPF flux confinement scaling. As can beseen in FIG. 19, based on measurements taken before and after t=0.5 ms,i.e., t≤0.5 ms and t>0.5 ms, the flux confinement (and similarly,particle confinement and energy confinement) scales with roughly thesquare of the electron Temperature (T_(e)) for a given separatrix radius(r_(s)). This strong scaling with a positive power of T_(e) (and not anegative power) is completely opposite to that exhibited by conventionaltokomaks, where confinement is typically inversely proportional to somepower of the electron temperature. The manifestation of this scaling isa direct consequence of the HPF state and the large orbit (i.e. orbitson the scale of the FRC topology and/or at least the characteristicmagnetic field gradient length scale) ion population. Fundamentally,this new scaling substantially favors high operating temperatures andenables relatively modest sized reactors.

With the advantages the HPF regime presents, FRC sustainment or steadystate driven by neutral beams is achievable, meaning global plasmaparameters such as plasma thermal energy, total particle numbers, plasmaradius and length as well as magnetic flux are sustainable at reasonablelevels without substantial decay. For comparison, FIG. 20 shows data inplot A from a representative HPF regime discharge in the FRC system 10as a function of time and in plot B for a projected representative HPFregime discharge in the FRC system 10 as a function of time where theFRC 450 is sustained without decay through the duration of the neutralbeam pulse. For plot A, neutral beams with total power in the range ofabout 2.5-2.9 MW were injected into the FRC 450 for an active beam pulselength of about 6 ms. The plasma diamagnetic lifetime depicted in plot Awas about 5.2 ms. More recent data shows a plasma diamagnetic lifetimeof about 7.2 ms is achievable with an active beam pulse length of about7 ms.

As noted above with regard to FIGS. 16A, 16B, 16C and 16D, thecorrelation between beam pulse length and FRC lifetime is not perfect asbeam trapping becomes inefficient below a certain plasma size, i.e., asthe FRC 450 shrinks in physical size not all of the injected beams areintercepted and trapped. Shrinkage or decay of the FRC is primarily dueto the fact that net energy loss (−4 MW about midway through thedischarge) from the FRC plasma during the discharge is somewhat largerthan the total power fed into the FRC via the neutral beams (−2.5 MW)for the particular experimental setup. As noted with regard to FIG. 3C,angled beam injection from the neutral beam guns 600 towards themid-plane improves beam-plasma coupling, even as the FRC plasma shrinksor otherwise axially contracts during the injection period. In addition,appropriate pellet fueling will maintain the requisite plasma density.

Plot B is the result of simulations run using an active beam pulselength of about 6 ms and total beam power from the neutral beam guns 600of slightly more than about 10 MW, where neutral beams shall inject H(or D) neutrals with particle energy of about 15 keV. The equivalentcurrent injected by each of the beams is about 110 A. For plot B, thebeam injection angle to the device axis was about 20°, target radius0.19 m. Injection angle can be changed within the range 15°-25°. Thebeams are to be injected in the co-current direction azimuthally. Thenet side force as well as net axial force from the neutral beam momentuminjection shall be minimized. As with plot A, fast (H) neutrals areinjected from the neutral beam injectors 600 from the moment the northand south formation FRCs merge in the confinement chamber 100 into oneFRC 450.

The simulations that where the foundation for plot B usemulti-dimensional hall-MHD solvers for the background plasma andequilibrium, fully kinetic Monte-Carlo based solvers for the energeticbeam components and all scattering processes, as well as a host ofcoupled transport equations for all plasma species to model interactiveloss processes. The transport components are empirically calibrated andextensively benchmarked against an experimental database.

As shown by plot B, the steady state diamagnetic lifetime of the FRC 450will be the length of the beam pulse. However, it is important to notethat the key correlation plot B shows is that when the beams are turnedoff the plasma or FRC begins to decay at that time, but not before. Thedecay will be similar to that which is observed in discharges which arenot beam-assisted—probably on order of 1 ms beyond the beam turn offtime—and is simply a reflection of the characteristic decay time of theplasma driven by the intrinsic loss processes.

Turning to FIGS. 21A, 21B, 21C, 21D and 21E, experiment resultsillustrated in the figures indicate achievement of FRC sustainment orsteady state driven by angled neutral beams, i.e., global plasmaparameters such as plasma radius, plasma density, plasma temperature aswell as magnetic flux are sustainable at constant levels without decayin correlation with NB pulse duration. For example, such plasmaparameters are essentially being kept constant for ˜5+ ms. Such plasmaperformance, including the sustainment feature, has a strong correlationNB pulse duration, with diamagnetism persisting even severalmilliseconds after NB termination due to the accumulated fast ions. Asillustrated, the plasma performance is only limited by the pulse-lengthconstraints arising from finite stored energies in the associated powersupplies of many critical systems, such as the NB injectors as well asother system components.

Neutral Beams Tunable Beam Energies

As noted above with regard to FIGS. 3A, 3B, 3C, 3D, 3E and 8, theneutral atom beams 600 are deployed on the FRC system 10 to provideheating and current drive as well as to develop fast particle pressure.The individual beam lines comprising neutral atom beam injector systems600 are located around the central confinement chamber 100 and, as shownin FIGS. 3C, 3D and 3E, are preferably angled to inject neutralparticles towards the mid-plane of the confinement chamber 100.

To further improve FRC sustainment and demonstrate FRC ramp-up to highplasma temperatures and elevated system energies, the present FRC system10 includes a neutral beam injector (NBI) system 600 of elevated powerand expanded pulse length, e.g., for exemplary purposes only, power ofabout 20+ MW with up to 30 ms pulse length. The NBI system 600 includesa plurality of positive-ion based injectors 615 (see FIGS. 3D and 3E)featuring flexible, modular design, with a subset of the NBI injectors615, e.g., four (4) of eight (8) NBI injectors 615, having a capabilityto tune the beam energy during a shot from an initial lower beam energyto an elevated beam energy, e.g., from about 15 keV to about 40 keV at aconstant beam current. This capability of the NBI injectors 615 isdesirable in order to achieve more efficient heat-up and resultantpressurization of the plasma core 450. In particular, this capabilityenables the highly desirable performance improvement at the peak energyoperating level compared to the low energy level: for example, (i)factor of up to 2× higher heating power; (ii) close to 5-fold reductionin charge exchange losses; and (iii) up to double the heatingefficiency. In addition, the continuously variable beam energyproducible by the NBI injectors 615 enables optimal matching of theorbital parameters of the injected and then trapped fast ions relativeto the instantaneous magnetic pressure profiles during the ramp-upprocess. Finally, fast ramp rates, allowing 0.1-10 ms ramp-up duration,together with fast (order of 1 ms or less) tunability of beam energy andpower of the NBI injectors 615 provides additional effective “controlknobs”, i.e., controllable features, for plasma shaping and activefeedback control of the plasma via modulation of beam energy and power.

Sufficient heating power is needed to enable heating and pressurizationof the FRC 450, both for sustainment as well as ramp-up to high plasmatemperatures and elevated system energies. Assuming sufficiently lowloss rates, the rate of ramp-up is mostly a function of how much powercan be deposited in the FRC core 450 by the NBI injectors 615 at anygiven time. Higher principal neutral beam power through the injectionport is, therefore, always desirable.

Moreover, the effective heating rate due to the NBI injectors 615 is acomplex interplay between the characteristics of the injected beam andthe then persistent instantaneous profiles of the temperatures of allspecies, electron and ion densities, neutral concentration, as well asmagnetic field across the FRC core 450. Of these the magnetic fieldprofiles are being deliberately changed on sub-millisecond timescalesduring ramp-up by a control system, while the kinetic pressure relatedprofiles evolve via intrinsic changes derivative of self-organizationprocesses and turbulence within the plasma as well as the energydeposited by the injection process. Tunability of the beams provides ameans to most optimally adapt to these varying conditions.

For instance, the charge exchange cross-section, i.e. the probability ofelectron capture by a fast ion to form a neutral atom, is a strongfunction of beam energy. For the range of 15-40 keV, the principalcharge exchange rate dramatically decreases as a function of beamenergy. Therefore, at any given level of field, the retention of energyin the plasma is highest when injecting the particles at the highestenergy compatible for such field level (amongst other things, thisrequires that the energy of the injected particles results in a trappedion orbit radius that fits within the inner wall of the confinementsystem).

Another example of the profile effects on overall heating efficiency hasto do with where power is deposited. Higher beam energy will typicallylead to relatively higher energy deposition in the FRC periphery versusthe core. Raising the magnetic field, but keeping the beam energy thesame, will results in tighter trapped ion orbits and commensuratelyhigher power coupling to the FRC core plasma. These facts then have astrong impact on energy retention as well—e.g. peripherally depositedenergy is much more readily transported out of the system along the openfield line structure, while core deposited energy is comparatively lostmore slowly due to the lower cross-field transport times. Thus, tightcoordination of magnetic field ramping and appropriate increases in beamenergy is desirable.

The beam system 600 is designed for fast ramping of voltage in the rangeof 0.1-10 ms. This provides the potential to increase ion and electrontemperatures by factors of 2 and 10, respectively, and do so ontimescales shorter than typical macroscopic instability growth times.Therefore, plasma stability is fundamentally increased, as isoperational reliability and reproducibility.

Variable voltage rise times of 0.05 to 1 ms provide sufficiently quickresponse times such that the beams can be utilized as part of an activefeedback system. In this way, beam modulation can be used to controlmacro and micro-stability. For instance, shifting momentarily the radialpower deposition profile by changing the beam energy (and therebyshifting the radial energy deposition pattern), one can affect pressuregradients that can counterbalance the onset of unstable plasma modes.The FRC system 10 shown in FIGS. 3D and 3E utilizes this capabilitytogether with fast magnetic feedback to control internal tilting,rotation rates, drift wave development and other operational scenarios.

FIG. 25 depicts an illustration of an NBI injector 615 of the presentFRC system 10. The NBI injector 615 is shown, in an exemplaryembodiment, to include: an arc driver 650; a plasma box 651; an ionoptical system 652, comprising a triode or tetrode grouping ofextraction and acceleration grids; an aiming gimbal 653; a neutralizer654, comprising arc evaporators 655, such as, e.g., Ti arc evaporators,a cryopump 656 having surface structures, such as, e.g., ribbed surfacestructures, configured for increased cryopumping, and a deflectingmagnet 656 for removing non-neutralized ions; and a collimating aperture658, including an insertable calorimeter 659 for intermittent beamcharacterization, diagnostics and recalibration.

More specifically and referring to FIG. 26, implementation of thetunable beam system, as shown, is preferably based on a triode type ionoptical system (=IOS) 660. The idea is an acceleration-decelerationscheme. As illustrated in the FIG. 26, a first grid G1 is set to avoltage V1, while the second grid G2 is set to a voltage V2 and thefinal grid G3 is set to voltage V3. The extracted ions are firstaccelerated to energy E1=e*(V1−V2) while traversing through the gapbetween G1 and G2 (e here refers to the electric charge of the ion).They are then decelerated in the gap between G2 and G3 such thatE2=E1+e*(V2−V3). The voltages are typically adjusted such that V1>V2<V3.Based on appropriate individual power supplies PS1, PS2, PS3, the gridvoltages can be incrementally adjusted during the pulse so as to changethe output of the emitted ions 662. For example, to begin a beam pulseof hydrogen atoms, the working voltages may be adjusted to V1=15 kV,V2=−25 kV and V3=0 V. The initial beam ions will then be acceleratedfirst to 40 keV and then emerge out of the IOS with an energy of 15 keV.Later in the pulse, the power supplies can be switched to provide V1=40kV, V2=−1 kV, V3=0 V. The beam deceleration in the second gap will thenbe practically absent, yielding an output beam energy of approximately40 keV. The power supplies are each individually controllable andprovide the appropriate voltage modulation. The initial beam ions aredrawn out of multitude of standard arch or RF based plasma source PS.Post emerging from IOS 660, the beam ions 662 traverse a neutralizer 664where the fast ions convert to neutral ions via charge exchange ofelectrons off the cold neutral gas present in the neutralizer 664.Proper cryopumping prevents neutral gas bleeding out of the downstreamorifice of the neutralizer 664. At the end of the neutralizer there isalso a proper bending magnet 666 that provides removal ofnon-neutralized fast ions 663 and an associated ion dump 668 to absorbthe fast ions and their energy. The emerging atom beam 670 is thenpassed through an appropriate aperture 6720to reduce beam divergence andprovide a well collimated stream of neutral atoms towards the core ofthe reactor.

In an alternate version, the IOS is based on a tetrode design. In thiscase the IOS consists of four grids that have the sameacceleration-deceleration principal as explained for the triode case.Those skilled in the art will readily recognize the similarity betweenthe system components and operating principles. The introduction of thefourth grid provides further fine-tuning possibilities and overall moreoperating flexibility.

The example embodiments provided herein have been described in U.S.Provisional Patent Application No. 62/414,574, which application isincorporated herein by reference.

Plasma Stability and Axial Position Control

Conventional solutions to FRC instabilities typically provide stabilityin the axial direction at the expense of being unstable in the radialdirection, or stability in the radial direction at the expense of beingaxially unstable, but not stability in both directions at the same time.To the first order, an equilibrium where the plasma position istransversally or radially stable has the desired property of beingaxisymmetric, at the expense of being axially unstable. In view of theforegoing, the embodiments provided herein are directed to systems andmethods that facilitate stability of an FRC plasma in both radial andaxial directions and axial position control of an FRC plasma along thesymmetry axis of an FRC plasma confinement chamber independent of theaxial stability properties of the FRC plasma's equilibrium. The axialposition instability, however, is actively controlled using a set ofexternal axisymmetric coils that control the FRC plasma axial position.The systems and methods provide feedback control of the FRC plasma axialposition independent of the stability properties of the plasmaequilibrium by acting on the voltages applied to a set of external coilsconcentric with the plasma and using a non-linear control technique.

The embodiments presented herein exploit an axially unstable equilibriaof the FRC to enforce radial stability, while stabilizing or controllingthe axial instability. In this way, stability in both axial and radialdirections can be obtained. The control methodology is designed to alterthe external or equilibrium magnetic field to make the FRC plasmaradially or transversally stable at the expense of being axiallyunstable, and then act on the radial field coil current in order toexpeditiously restore the FRC plasma position towards the mid-planewhile minimizing overshooting and/or oscillations around the mid-planeof the confinement chamber. The advantage of this solution is that itreduces the complexity of the actuators required for control. Comparedwith the conventional solutions with multiple degrees of freedom, themethodology of the embodiment presented herein reduces the complexity toa control problem along the FRC plasma revolution axis having one degreeof freedom.

The combination of waveforms in coil currents, fueling and neutral beampower that result into an axially unstable plasma define the plasmacontrol scenario that sets the plasma into an axial unstable situation.The scenario can be pre-programmed using prior knowledge of simulationsor experiments, or feedback controlled to maintain an equilibrium thatis axially unstable. The plasma position should be controlled during thedischarges independently of the stability properties of the equilibrium,e.g. the control scheme should work for either axially stable or axiallyunstable plasmas, up to a limit. The most axially unstable plasma thatcan be controlled has a growth time comparable to the skin time of thevessel.

Turning now to the systems and methods that facilitate stability of anFRC plasma in both radial and axial directions and axial positioncontrol of an FRC plasma along the symmetry axis of an FRC plasmaconfinement chamber, FIG. 27 shows a simplified scheme to illustrate anexample embodiment of an axial position control mechanism 510. Arotating FRC plasma 520 shown within a confinement chamber 100 has aplasma current 522 and an axial displacement direction 524. Anequilibrium field (not shown) is produced within the chamber 100 bysymmetric current components such as, e.g., the quasi-dc coils 412 (seeFIGS. 2, 3A, 3D and 3E). The equilibrium field does not produce a netforce in the axial displace direction 524, but can be tuned to produceeither a transversally/radially or axially stable plasma. For thepurposes of the embodiment presented herein, the equilibrium field istuned to produce a transversally/radially stable FRC plasma 520. Asnoted above, this results in axial instability and, thus, axialdisplacement of the FRC plasma 520 in an axial displacement direction524. As the FRC plasma 520 moves axially it induces current 514 and 516that are antisymmetric, i.e., in counter directions in the walls of theconfinement chamber 100 on each side of the mid-plane of the confinementchamber 100. The FRC plasma 520 will induce these type of currentcomponents in both the vessel and also in the external coils. Theseantisymmetric current components 514 and 516 produce a radial fieldwhich interacts with the toroidal plasma current 522 to produce a forcethat opposes the movement of the FRC plasm 520, and the result of thisforce is that it slows down plasma axial displacements. These currents514 and 516 gradually dissipate with time, due to the resistivity of theconfinement chamber 100.

Radial field coils 530 and 531 disposed about the confinement chamber100 on each side of the mid-plane provide additional radial fieldcomponents that are due to the currents 532 and 534 induced in counterdirections in the coils 530 and 531. The radial field coils 530 and 531may comprise a set of axisymmetric coils that may be positioned internalor external to the containment vessel 100. The radial coils 530 and 531are shown to be positioned external to the containment vessel 100similar to the quasi-dc coils 412 (see, FIGS. 2, 3A, 3D and 3E). Each ofthe coils 530 and 531, or sets of coils, may carry a different currentthan the coils on the opposite side of the mid-plane, but the currentsare antisymmetric with respect to the mid-plane of the containmentvessel 100 and produce a magnetic field structure with B_(z)≠0, B_(r)=0along the midplane. The radial field coils 530 and 531 create asupplemental radial field component that interacts with the toroidalplasma current 522 to produce an axial force. The axial force in turnmoves the plasma back towards the mid-plane of the confinement chamber100.

The control mechanism 510 includes a control system configured to act onthe radial field coil current in order to expeditiously restore theplasma position towards the mid-plane while minimizing overshootingand/or oscillations around the machine mid-plane. The control systemincludes a processor operably coupled to the radial field coils 530 and531, the quasi-dc coils 412, their respective power supplies, and othercomponents such as, e.g., magnetic sensors, providing plasma position,plasma velocity, and active coil current measurements. The processor maybe configured to perform the computations and analyses described in thepresent application and may include or be communicatively coupled to oneor more memories including non-transitory computer readable medium. Itmay include a processor-based or microprocessor-based system includingsystems using microcontrollers, reduced instruction set computers(RISC), application specific integrated circuits (ASICs), logiccircuits, and any other circuit or processor capable of executing thefunctions described herein. The above examples are exemplary only, andare thus not intended to limit in any way the definition and/or meaningof the term “processor” or “computer.”

Functions of the processor may be implemented using either softwareroutines, hardware components, or combinations thereof. The hardwarecomponents may be implemented using a variety of technologies,including, for example, integrated circuits or discrete electroniccomponents. The processor unit typically includes a readable/writeablememory storage device and typically also includes the hardware and/orsoftware to write to and/or read the memory storage device.

The processor may include a computing device, an input device, a displayunit and an interface, for example, for accessing the Internet. Thecomputer or processor may include a microprocessor. The microprocessormay be connected to a communication bus. The computer or processor mayalso include a memory. The memory may include Random Access Memory (RAM)and Read Only Memory (ROM). The computer or processor may also include astorage device, which may be a hard disk drive or a removable storagedrive such as a floppy disk drive, optical disk drive, and the like. Thestorage device may also be other similar means for loading computerprograms or other instructions into the computer or processor.

The processor executes a set of instructions that are stored in one ormore storage elements, in order to process input data. The storageelements may also store data or other information as desired or needed.The storage element may be in the form of an information source or aphysical memory element within a processing machine.

The problem of controlling the position of an axially stable or unstableFRC configuration using the radial field coil actuators is solved usinga branch of non-linear control theory known as sliding mode control. Alinear function of system states (the sliding surface) acts as the errorsignal with the desired asymptotically stable (sliding) behavior. Thesliding surface is designed using Liapunov theory to exhibit asymptoticstability in a broad range of FRC dynamic parameters. The proposedcontrol scheme can then be used for both axially stable and unstableplasmas without the need to re-tune the parameters used in the slidingsurface. This property is advantageous because, as mentioned before, theequilibrium may have to transit between axially stable and axiallyunstable equilibria on different phases of the FRC discharge.

The configuration of the control scheme 500 is shown in FIG. 28. The lowpass filter restricts the switching frequencies within the desiredcontrol bandwidth. A digital control loop requiring sampling and signaltransmission with one sample delay is assumed. The error signal (thesliding surface) is a linear combination of coil current, plasmaposition and plasma velocity. Plasma position and velocity of the plasmaare obtained from external magnetic measurements. Currents in the activecoil systems can be measured by standard methods.

Coil currents and plasma position are required to implement the positioncontrol. Plasma velocity is required to improve performance but isoptional. A non-linear function of this error signal (relay control law)generates discrete voltage levels for every pair of power suppliesconnected to mid-plane symmetric coils. Midplane symmetric coils arefeed with relay voltages of same intensity but opposite sign. Thiscreates a radial field component to restore the plasma position towardsthe mid-plane.

To demonstrate the feasibility of the control scheme, a rigid plasmamodel is used to simulate the plasma dynamics. The model utilizes amagnet geometry. Plasma current distribution corresponds to axiallyunstable equilibria with a growth time of 2 ms when only plasma andvessel are considered. The power supplies are assumed to work withdiscrete voltage levels, typically in 800 V steps.

FIG. 29 shows several plasma control simulations that highlight therelationship between applied voltages to the coils, and the plasmaposition settling times, along with the required coil peak current andramp rates to bring back to the mid-plane a plasma that was displacedaxially by 20 cm. These sliding mode axial position control simulationexamples are run at 0.3 T using four pairs of external trim coils. Fourcases are shown corresponding with power supplies with discrete voltagelevels in steps of 200 V (solid square), 400V (solid circle), 800 V(solid triangle) and 1600 V (hollow square). For all four cases thecontrol bandwidth is 16 kHz and sampling frequency is 32 kHz. The plasmaposition (top figure), current in the outermost coil pair (middle) andcoil current ramp-rate (bottom) are shown. Plasma displacement isallowed to grow unstable until it reaches 20 cm. At this point thefeedback control is applied.

Simulation results indicate that:

-   -   1. To bring the plasma back to the mid-plane within 5 ms (solid        sqaure traces), coil ramp-up rate of 0.5 MA/s suffices,        requiring a 200 V power supply.    -   2. To bring the plasma back to the mid-plane within 2.3 ms        (solid circle traces), coil ramp-up rate of 1 MA/s suffices,        requiring a 400 V power supply.    -   3. To bring the plasma back to the mid-plane within 1.3 ms        (solid triangle traces), coil ramp-up rate of 2 MA/s suffices,        requiring an 800 V power supply.    -   4. To bring the plasma back to the mid-plane within 1.0 ms        (hollow square traces), coil ramp-up rate of 4 MA/s suffices,        requiring a 1600 V power supply.

The peak currents for all the trim coils for the third case studiedabove (the 2 MA/s ramp rate case) are also shown in FIG. 30 as functionof trim coil position. The sliding mode axial position controlsimulation examples are run at 0.3 T using four pairs of external trimcoils using a power supply with three levels (+800V,0,−800V), a controlbandwidth of 16 kHz and a sampling rate of 32 kHz. To bring the plasmaback to the mid-plane within 1.3 ms, coil ramp-up rate of 2 MA/s isrequired. The peak current required in all coil pair is less than 1.5kA. The actual switching frequency required (about 2 kHz) is well belowthe control system bandwidth

The control system can also be implemented a target surface which isfunction of coil current and plasma velocity alone, without plasmaposition. In this case the axial position control loop provides onlystabilization of the axial dynamics, but not control. This means thatthe plasma is in a metastable situation and can drift slowly along itsaxis. The position control is then provided using an additional feedbackloop that controls the plasma gaps between plasma separatrix and vessel,hence it performs plasma shape and position control simultaneously.

Another plasma confinement device where similar control systems are usedis the tokamak. To maintain plasma confinement, the plasma current in atokamak must be kept between a lower and an upper limit that are roughlyproportional to plasma density and toroidal field, respectively. Tooperate at high plasma density plasma current must be increased. At thesame time the poloidal field must be kept as low as possible so the qsafety factor is above q=2. This is achieved by elongating the plasmaalong the machine axis direction, allowing to fit large plasma current(and hence allow high plasma density) without increasing the boundarymagnetic field above its safety limits. These elongated plasmas areunstable along the machine axis direction (known in tokamak jargon asthe vertical direction), and also require plasma stabilizationmechanisms. Vertical plasma position control in tokamaks is alsorestored using a set of radial field coils, so it strongly resembles theRFC position control problem. However, the reasons to requirestabilization in a tokamak and an FRC are different. In a tokamak plasmavertical instability is a penalty to be paid to operate at large plasmacurrent, which requires plasma elongation to operate with high toroidalfield. In the case of the FRC, plasma instability is a penalty to bepaid to obtain transverse stability. Tokamaks have toroidal field thatstabilizes the configuration, so they don't need transversestabilization.

According to an embodiment of the present disclosure, a method forgenerating and maintaining a magnetic field with a field reversedconfiguration (FRC) comprising forming an FRC about a plasma in aconfinement chamber, and injecting a plurality of neutral beams into theFRC plasma while tuning the beam energies of the plurality of neutralbeams between a first beam energy and a second beam energy, wherein thesecond beam energy differs from the first beam energy.

According to a further embodiment of the present disclosure, the secondbeam energy is higher than the first beam energy.

According to a further embodiment of the present disclosure, theplurality of neutral beams switch between the first and second beamenergies during the duration of an injection shot.

According to a further embodiment of the present disclosure, the firstand second beam energies are in the range of about 15 to 40 keV.

According to a further embodiment of the present disclosure, the methodfurther comprising controlling the beam energies of the plurality ofneutral beams by a feedback signal received from an active feedbackplasma control system.

According to a further embodiment of the present disclosure, the methodfurther comprising controlling the beam energies of the plurality ofneutral beams by a feedback signal received from an active feedbackplasma control system.

According to a further embodiment of the present disclosure, controllingthe beam energies of the plurality of neutral beams includes adjustingthe beam energies of the plurality of neutral beams to adjust the radialbeam power deposition profile to adjust the pressure gradient value.

According to a further embodiment of the present disclosure, the methodfurther includes maintaining the FRC at or about a constant valuewithout decay and elevating the plasma temperature to above about 1.0keV by injecting beams of fast neutral atoms from neutral beam injectorsinto the FRC plasma at an angle towards the mid through plane of theconfinement chamber.

According to a further embodiment of the present disclosure, elevatingthe plasma temperature includes elevating the temperature from about 1.0keV to about 3.0 keV.

According to a further embodiment of the present disclosure, elevatingthe plasma temperature includes elevating the temperature from about 1.0keV to about 3.0 keV.

According to a further embodiment of the present disclosure, the methodfurther comprising generating a magnetic field within the confinementchamber with quasi dc coils extending about the confinement chamber anda mirror magnetic field within opposing ends of the confinement chamberwith quasi dc mirror coils extending about the opposing ends of theconfinement chamber.

According to a further embodiment of the present disclosure, the methodfurther comprising generating a magnetic field within the confinementchamber with quasi dc coils extending about the confinement chamber anda mirror magnetic field within opposing ends of the confinement chamberwith quasi dc mirror coils extending about the opposing ends of theconfinement chamber.

According to a further embodiment of the present disclosure, forming theFRC includes forming a formation FRC in opposing first and secondformation sections coupled to the confinement chamber and acceleratingthe formation FRC from the first and second formation sections towardsthe mid through plane of the confinement chamber where the two formationFRCs merge to form the FRC.

According to a further embodiment of the present disclosure, forming theFRC includes one of forming a formation FRC while accelerating theformation FRC towards the mid through plane of the confinement chamberand forming a formation FRC then accelerating the formation FRC towardsthe mid through plane of the confinement chamber.

According to a further embodiment of the present disclosure,accelerating the formation FRC from the first and second formationsections towards the mid through plane of the confinement chamberincludes passing the formation FRC from the first and second formationsections through first and second inner divertors coupled to oppositeends of the confinement chamber interposing the confinement chamber andthe first and second formation sections.

According to a further embodiment of the present disclosure, passing theformation FRC from the first and second formation sections through firstand second inner divertors includes inactivating the first and secondinner divertors as the formation FRC from the first and second formationsections passes through the first and second inner divertors.

According to a further embodiment of the present disclosure, the methodfurther comprising guiding magnetic flux surfaces of the FRC into thefirst and second inner divertors.

According to a further embodiment of the present disclosure, the methodfurther comprising guiding magnetic flux surfaces of the FRC into firstand second outer divertors coupled to the ends of the formationsections.

According to a further embodiment of the present disclosure, the methodfurther comprising generating a magnetic field within the formationsections and the first and second outer divertors with quasi-dc coilsextending about the formation sections and divertors.

According to a further embodiment of the present disclosure, the methodfurther comprising generating a magnetic field within the formationsections and first and second inner divertors with quasi-dc coilsextending about the formation sections and divertors.

According to a further embodiment of the present disclosure, the methodfurther comprising generating a mirror magnetic field between the firstand second formation sections and the first and second outer divertorswith quasi-dc mirror coils.

According to a further embodiment of the present disclosure, the methodfurther comprising generating a mirror plug magnetic field within aconstriction between the first and second formation sections and thefirst and second outer divertors with quasi-dc mirror plug coilsextending about the constriction between the formation sections and thedivertors.

According to a further embodiment of the present disclosure, the methodfurther comprising generating a mirror magnetic field between theconfinement chamber and the first and second inner divertors withquasi-dc mirror coils and generating a necking magnetic field betweenthe first and second formation sections and the first and second innerdivertors with quasi-dc low profile necking coils.

According to a further embodiment of the present disclosure, the methodfurther comprising generating one of a magnetic dipole field and amagnetic quadrupole field within the chamber with saddle coils coupledto the chamber.

According to a further embodiment of the present disclosure, the methodfurther comprising conditioning the internal surfaces of the chamber andthe internal surfaces of first and second formation sections, first andsecond divertors interposing the confinement chamber and the first andsecond formation sections, and first and second outer divertors coupledto the first and second formation sections with a gettering system.

According to a further embodiment of the present disclosure, thegettering system includes one of a Titanium deposition system and aLithium deposition system.

According to a further embodiment of the present disclosure, the methodfurther comprising axially injecting plasma into the FRC from axiallymounted plasma guns.

According to a further embodiment of the present disclosure, the methodfurther comprising controlling the radial electric field profile in anedge layer of the FRC.

According to a further embodiment of the present disclosure, controllingthe radial electric field profile in an edge layer of the FRC includesapplying a distribution of electric potential to a group of open fluxsurfaces of the FRC with biasing electrodes.

According to a further embodiment of the present disclosure, the methodfurther comprising stabilizing the FRC plasma in a radial directionnormal to a longitudinal axis of the confinement chamber to position theFRC plasma axisymmetric about the longitudinal axis and in an axialdirection along the longitudinal axis to position the FRC plasmaaxisymmetric about a mid-plane of the confinement chamber.

According to a further embodiment of the present disclosure, the methodfurther comprising generating an applied magnetic field within thechamber with quasi-dc coils extending about the chamber.

According to a further embodiment of the present disclosure, the methodfurther comprising stabilizing the FRC plasma in the radial directionincludes tuning the applied magnetic field to induce radial stabilityand axial instability in the FRC plasma.

According to a further embodiment of the present disclosure, axiallystabilizing the FRC plasma includes creating first and second radialmagnetic fields, wherein the first and second radial magnetic fieldsinteract with the FRC to axially move the FRC plasma to to position theFRC plasma axisymmetric about the mid-plane.

According to a further embodiment of the present disclosure, the methodfurther comprising injecting compact toroid (CT) plasmas from first andsecond CT injectors into the FRC plasma at an angle towards themid-plane of the confinement chamber, wherein the first and second CTinjectors are diametrically opposed on opposing sides of the mid-planeof the confinement chamber.

According to a further embodiment of the present disclosure, a systemfor generating and maintaining a magnetic field with a field reversedconfiguration (FRC) comprising: a confinement chamber; first and seconddiametrically opposed FRC formation sections coupled to the first andsecond diametrically opposed inner divertors; first and second divertorscoupled to the first and second formation sections; one or more of aplurality of plasma guns, one or more biasing electrodes and first andsecond mirror plugs, wherein the plurality of plasma guns includes firstand second axial plasma guns operably coupled to the first and seconddivertors, the first and second formation sections and the confinementchamber, wherein the one or more biasing electrodes being positionedwithin one or more of the confinement chamber, the first and secondformation sections, and the first and second outer divertors, andwherein the first and second mirror plugs being position between thefirst and second formation sections and the first and second divertors;a gettering system coupled to the confinement chamber and the first andsecond divertors; a plurality of neutral atom beam injectors coupled tothe confinement chamber and angled toward a mid-plane of the confinementchamber, wherein one or more of the plurality of neutral atom beaminjectors are tunable between a first beam energy and a second beamenergy, wherein the second beam energy differ from the first beamenergy; and a magnetic system comprising a plurality of quasi-dc coilspositioned around the confinement chamber, the first and secondformation sections, and the first and second divertors, and first andsecond set of quasi-dc mirror coils positioned between the first andsecond formation sections and the first and second divertors.

According to a further embodiment of the present disclosure, the secondbeam energy is higher than the first beam energy.

According to a further embodiment of the present disclosure, theplurality of neutral beams are configured to switch between the firstand second beam energies during the duration of an injection shot.

According to a further embodiment of the present disclosure, the firstand second beam energies are in the range of about 15 to 40 keV.

According to a further embodiment of the present disclosure, the systemfurther comprising an active feedback plasma control system configuredto control the beam energies of the plurality of neutral beams.

According to a further embodiment of the present disclosure, the systemis configured to generate an FRC and maintain the FRC without decaywhile the neutral beams are injected into the plasma and elevate theplasma temperature to about 1.0 keV to 3.0 keV.

According to a further embodiment of the present disclosure, the firstand second divertors comprise first and second inner divertorsinterposing the first and second formation sections and the confinementchamber, and further comprising first and second outer divertors coupledto the first and second formation sections, wherein the first and secondformation sections interposing the first and second inner divertors andthe first and second outer divertors.

According to a further embodiment of the present disclosure, the systemfurther comprising first and second axial plasma guns operably coupledto the first and second inner and outer divertors, the first and secondformation sections and the confinement chamber.

According to a further embodiment of the present disclosure, the systemfurther comprising two or more saddle coils coupled to the confinementchamber.

According to a further embodiment of the present disclosure, theformation section comprises modularized formation systems for generatingan FRC and translating it toward a midplane of the confinement chamber.

According to a further embodiment of the present disclosure, the biasingelectrodes includes one or more of one or more point electrodespositioned within the containment chamber to contact open field lines, aset of annular electrodes between the confinement chamber and the firstand second formation sections to charge far-edge flux layers in anazimuthally symmetric fashion, a plurality of concentric stackedelectrodes positioned in the first and second divertors to chargemultiple concentric flux layers, and anodes of the plasma guns tointercept open flux.

According to a further embodiment of the present disclosure, the systemfurther comprising a control system operably coupled to the quasi-dccoils and the first and second radial magnetic field coils, the controlsystem including a processor coupled to a non-transitory memorycomprising a plurality of instruction that when executed causes theprocessor to tune the magnetic field generated by the plurality ofquasi-dc coils and the first and second radial field coils to stabilizean FRC plasma in a radial direction normal to a longitudinal axis of thechamber to position the FRC plasma axisymmetric about the longitudinalaxis and in an axial direction along the longitudinal axis to positionthe FRC plasma axisymmetric about the mid-plane.

According to a further embodiment of the present disclosure, the systemis configured to generate an FRC and maintain the FRC at or about aconstant value without decay while neutral atom beams are injected intothe FRC.

According to a further embodiment of the present disclosure, the firstand second radial magnetic fields are antisymmetric about the mid-plane.

According to a further embodiment of the present disclosure, the systemfurther comprising first and second compact toroid (CT) injectorscoupled to the confinement chamber at an angle towards the mid-plane ofthe confinement chamber, wherein the first and second CT injectors arediametrically opposed on opposing sides of the mid-plane of theconfinement chamber.

The example embodiments provided herein, however, are merely intended asillustrative examples and not to be limiting in any way.

All features, elements, components, functions, and steps described withrespect to any embodiment provided herein are intended to be freelycombinable and substitutable with those from any other embodiment. If acertain feature, element, component, function, or step is described withrespect to only one embodiment, then it should be understood that thatfeature, element, component, function, or step can be used with everyother embodiment described herein unless explicitly stated otherwise.This paragraph therefore serves as antecedent basis and written supportfor the introduction of claims, at any time, that combine features,elements, components, functions, and steps from different embodiments,or that substitute features, elements, components, functions, and stepsfrom one embodiment with those of another, even if the followingdescription does not explicitly state, in a particular instance, thatsuch combinations or substitutions are possible. Express recitation ofevery possible combination and substitution is overly burdensome,especially given that the permissibility of each and every suchcombination and substitution will be readily recognized by those ofordinary skill in the art upon reading this description.

In many instances, entities are described herein as being coupled toother entities. It should be understood that the terms “coupled” and“connected” (or any of their forms) are used interchangeably herein and,in both cases, are generic to the direct coupling of two entities(without any non-negligible (e.g., parasitic) intervening entities) andthe indirect coupling of two entities (with one or more non-negligibleintervening entities). Where entities are shown as being directlycoupled together, or described as coupled together without descriptionof any intervening entity, it should be understood that those entitiescan be indirectly coupled together as well unless the context clearlydictates otherwise.

While the embodiments are susceptible to various modifications andalternative forms, specific examples thereof have been shown in thedrawings and are herein described in detail. It should be understood,however, that these embodiments are not to be limited to the particularform disclosed, but to the contrary, these embodiments are to cover allmodifications, equivalents, and alternatives falling within the spiritof the disclosure. Furthermore, any features, functions, steps, orelements of the embodiments may be recited in or added to the claims, aswell as negative limitations that define the inventive scope of theclaims by features, functions, steps, or elements that are not withinthat scope.

1. A method for generating and maintaining a magnetic field with a fieldreversed configuration (FRC) comprising the steps of: forming an FRCabout a plasma in a confinement chamber, and injecting a plurality ofneutral beams into the FRC plasma while tuning the beam energies of theplurality of neutral beams between a first beam energy and a second beamenergy, wherein the second beam energy differs from the first beamenergy, wherein the second beam energy is higher than the first beamenergy. 2-3. (canceled)
 4. The method of claim 1, wherein the first andsecond beam energies are in the range of about 15 to 40 keV.
 5. Themethod of claim 1, further comprising the step of controlling the beamenergies of the plurality of neutral beams by a feedback signal receivedfrom an active feedback plasma control system.
 6. (canceled)
 7. Themethod of claim 5, wherein the step of controlling the beam energies ofthe plurality of neutral beams includes adjusting the beam energies ofthe plurality of neutral beams to adjust the radial beam powerdeposition profile to adjust the pressure gradient value.
 8. The methodof claim 6, wherein the step of controlling the beam energies of theplurality of neutral beams includes adjusting the beam energies of theplurality of neutral beams to adjust the radial beam power depositionprofile to adjust the pressure gradient value.
 9. The method of claim 1,further includes maintaining the FRC at or about a constant valuewithout decay and elevating the plasma temperature to above about 1.0keV by injecting beams of fast neutral atoms from neutral beam injectorsinto the FRC plasma at an angle towards the mid through plane of theconfinement chamber. 10-11. (canceled)
 12. The method of claim 9,wherein the step of elevating the plasma temperature includes elevatingthe temperature from about 1.0 keV to about 3.0 keV. 13-15. (canceled)16. The method of claim 1, wherein the step of the forming the FRCincludes forming a formation FRC in opposing first and second formationsections coupled to the confinement chamber and accelerating theformation FRC from the first and second formation sections towards themid through plane of the confinement chamber where the two formationFRCs merge to form the FRC. 17-18. (canceled)
 19. The method of claim16, wherein the step of accelerating the formation FRC from the firstand second formation sections towards the mid through plane of theconfinement chamber includes passing the formation FRC from the firstand second formation sections through first and second inner divertorscoupled to opposite ends of the confinement chamber interposing theconfinement chamber and the first and second formation sections.
 20. Themethod of claim 19, wherein the step of passing the formation FRC fromthe first and second formation sections through first and second innerdivertors includes inactivating the first and second inner divertors asthe formation FRC from the first and second formation sections passesthrough the first and second inner divertors.
 21. The method of claim19, further comprising the step of guiding magnetic flux surfaces of theFRC into the first and second inner divertors. 22-27. (canceled)
 28. Themethod of claim 9, further comprising the step of generating one of amagnetic dipole field and a magnetic quadrupole field within the chamberwith saddle coils coupled to the chamber.
 29. (canceled)
 30. The methodof claim 9, further comprising the step of conditioning the internalsurfaces of the chamber and the internal surfaces of first and secondformation sections, first and second divertors interposing theconfinement chamber and the first and second formation sections, andfirst and second outer divertors coupled to the first and secondformation sections with a gettering system. 31-32. (canceled)
 33. Themethod of claim 9 further comprising the step of controlling the radialelectric field profile in an edge layer of the FRC.
 34. The method ofclaim 33, wherein the step of controlling the radial electric fieldprofile in an edge layer of the FRC includes applying a distribution ofelectric potential to a group of open flux surfaces of the FRC withbiasing electrodes.
 35. The method of claim 1, further comprising thestep of stabilizing the FRC plasma in a radial direction normal to alongitudinal axis of the confinement chamber to position the FRC plasmaaxisymmetric about the longitudinal axis and in an axial direction alongthe longitudinal axis to position the FRC plasma axisymmetric about amid-plane of the confinement chamber.
 36. The method of claim 35 furthercomprising the step of generating an applied magnetic field within thechamber with quasi-dc coils extending about the chamber.
 37. The methodof claim 35 wherein the step of stabilizing the FRC plasma in the radialdirection includes tuning the applied magnetic field to induce radialstability and axial instability in the FRC plasma.
 38. The method ofclaim 35 wherein the step of axially stabilizing the FRC plasma includescreating first and second radial magnetic fields, wherein the first andsecond radial magnetic fields interact with the FRC to axially move theFRC plasma to to position the FRC plasma axisymmetric about themid-plane.
 39. The method of claim 1, further comprising injectingcompact toroid (CT) plasmas from first and second CT injectors into theFRC plasma at an angle towards the mid-plane of the confinement chamber,wherein the first and second CT injectors are diametrically opposed onopposing sides of the mid-plane of the confinement chamber. 40-60.(canceled)